Equations

If $\displaystyle \frac{3}{x+y} + \frac{2}{x-y} = -1$ and $\displaystyle \frac{1}{x+y} - \frac{1}{x-y} = \frac{4}{3}$ then $\displaystyle (x, y)$ is:

$\displaystyle \frac{2x+5}{10} + \frac{3x+10}{15} = 5$, find $\displaystyle x$

Find value of $\displaystyle x^2 - 10x + 1$ if $\displaystyle x = \frac{1}{5-2\sqrt{6}}$

The cost of $\displaystyle 2$ oranges and $\displaystyle 3$ apples is $\displaystyle 28$. If the cost of an apple is doubled then the cost of $\displaystyle 3$ oranges and $\displaystyle 5$ apples is $\displaystyle 75$. The original cost of $\displaystyle 7$ oranges and $\displaystyle 4$ apples (in Rs) is:

In a multiple choice question paper consisting of $\displaystyle 100$ questions of $\displaystyle 1$ mark each, a candidate gets $\displaystyle 60\%$ marks. If the candidate attempted all questions and there was a penalty of $\displaystyle 0.25$ marks for wrong answers is:

The values of $\displaystyle x$ and $\displaystyle y$ satisfying the equations $\displaystyle \frac{3}{x+y} + \frac{2}{x-y} = 3$ and $\displaystyle \frac{2}{x+y} + \frac{3}{x-y} = \frac{23}{3}$ given by

A plumber can be paid either $\displaystyle 600$ and $\displaystyle 50$ per hour or $\displaystyle 170$ per hour. If the job takes '$\displaystyle n$' hour, for what value of '$\displaystyle n$' the second method earns better wages for the plumber?

The solution of the following system of linear eqs. $\displaystyle 2x - 5y + 4 = 0$ and $\displaystyle 2x + y - 8 = 0$ will be:

The solution of the linear simultaneous equations $\displaystyle 2x - y = 4$ and $\displaystyle 3x + 4y = 17$ is

A person purchased $\displaystyle 2$ apples and $\displaystyle 5$ bananas at the cost of $\displaystyle 90$. Later he visited to another shop where shopkeeper told him that if you give me $\displaystyle 50$ and one banana, I can give you $\displaystyle 3$ apples. He agreed to the deal. What is the cost of one apple and one banana?

In the above table corresponding values of two variable $\displaystyle x$ and $\displaystyle y$ have been given. Which of the following equations establishes the relationship between the two variables?$\displaystyle \begin{array}{|c|c|c|c|c|}\hline x & 5 & 6 & 7 & 8 \\ \hline y & 11 & 13 & 15 & 17 \\ \hline \end{array}$

If $\displaystyle 2x - 3y = 1$ and $\displaystyle 5x + 2y = 50$, then what is the value of $\displaystyle (x-2y)$?

If $\displaystyle xy + yz + zx = -1$, then the value of $\displaystyle \frac{x+y}{1+xy} + \frac{y+z}{1+yz} + \frac{z+x}{1+zx}$ is

The value of 'k' for system of equations $\displaystyle kx+2y = 5$ and $\displaystyle 3x+y = 1$ has no solution is

The cab bill is partly fixed and partly varies on the distance covered. For $\displaystyle 456$ km the bill is $\displaystyle 8252$, for $\displaystyle 484$ km the bill is Rs. $\displaystyle 8728$. What will the bill be for $\displaystyle 500$km?

The point of intersection between the lines $\displaystyle 3x+4y = 7$ and $\displaystyle 4x-y = 3$ lie in the

If $\displaystyle \sqrt{\frac{1}{25}} = 1 + \frac{x}{144}$, then $\displaystyle x$ is

$\displaystyle 2x + 5 + \frac{3x+10}{15} = 5$, then the value of $\displaystyle x$

Solve for $\displaystyle x, y$ and $\displaystyle z$.$\displaystyle \frac{xy}{x+y} = 210$, $\displaystyle \frac{yz}{y+z} = 140$, $\displaystyle \frac{xz}{x+z} = 120$

If $\displaystyle \sqrt{x+5} + \sqrt{x-16} = \frac{7}{\sqrt{x+5} - \sqrt{x-16}}$ then $\displaystyle x$ equals

If $\displaystyle 2^{x+y} = 2^{x-y} = \sqrt{8}$, then the value of $\displaystyle x$ and $\displaystyle y$ is

If the sides of an equilateral triangle are shortened by 3 units, 4 units and 5 units respectively and a right triangle is formed then the side of an equilateral triangle is:

A number consist of two digits such that the digit in one's place in thrice the digit in ten's place. If 36 be added then the digits are reversed. Find the number ____.

If a person has cloth of total 91 cm. If he divides it into 3 parts then longest part is twice the shortest one and another part is 3 cm more than shortest one. What is the shortest one?

If the cost of 3 bags and 4 pens is $\displaystyle 257$ whereas the cost of 4 bags and 3 pens is $\displaystyle 324$, then the cost of one bag is:

The largest side of a triangle is 3 times the shortest side and third side is 4 cm shorter then largest side. If the perimeter of the triangle is at least 59 cm, what is the length of shortest side?

The age of a man is four times the sum of the ages of his two sons and after 10 years, his age will be double the sum of their ages. The present age of the man must be

Divide 27 into two parts, so that 5 times the first and 11 times the second together equal to 195, then the ratio of first and second part is:

A number consist of two digits. The digits in the ten's place is 3 times the digit in the unit's place. If 54 is subtracted from the number, then the digits are reversed. The number is:

A number consist of two digits. The digits in tens place is 3 times the digit in the unit's place. If 54 is subtracted from the digits are reversed. The number is

A number consist of three digit of which the middle one is zero and the sum of other digits is 9. The number formed by interchanging the first and third digits is more than the original number by 297 find the number?

The age of a person is twice the sum of the ages of his two sons and 5 years ago his age was thrice the sum of their ages. Find present age.

Ten years ago the age of a father was four times his son. Ten years hence the age of the father will be twice that of his son. The present age of the father and the son are

3 Chairs and 3 tables cost $\displaystyle 370$. What is the cost of the table and two chairs?

If thrice of A's age 6 years ago be subtracted from twice his present age, the result would be equal to his present age. Find A's Age

The sum of two numbers is 62 and their product is 960. The sum of their reciprocals is

Three persons Mr. Roy, Mr. Paul and Mr. Singh together have $\displaystyle 51$. Mr. Paul has $\displaystyle 4$ less than Mr. Roy and Mr. Singh has $\displaystyle 5$ less than Mr. Roy. They have the money as:

The wages of 8 men and 6 boys amount to $\displaystyle 33$. If 4 men earn $\displaystyle 4.50$ more than 5 boys determine the wages of each man and boy

The cost of 5 mangoes is equal to the cost of 20 oranges. If the total cost 2 mangoes and 10 oranges is $\displaystyle 22.50$, find the cost of two oranges.

A man sells 6 radios and 4 televisions for $\displaystyle 18,480$. If 14 radios and 2 televisions are sold for the same. What is the price of radio?

On the average an experienced person does 7 units of work while a fresh one work 5 units of work daily but the employer has to maintain an output of atleast 35 units of work per day. The situation can be expressed as:

X and Y have their present ages in the ratio $\displaystyle 6:7$. 14 years ago, the ratio of the ages of the two was $\displaystyle 1:5$. What will be the ratio of their ages 21 years from now?

A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and third length is to be twice as the shortest. What is the possible length for the shortest piece?

If thrice of A's age 6 years ago be subtracted from twice his present age, the result would be equal to his present age. Find A's present age.

The cost prices of 3 pens and 4 bags is $\displaystyle 324$, and 4 pens and 3 bags is $\displaystyle 257$, then cost price of 1 pen is equal to

In a hostel ration stocked for 400 students upto 31 days. After 28 days 280 students were vacated the hostel. Find the number of days for which the remaining ration will be sufficient for the remaining students.

The sum of the two numbers is 80 and the sum of their squares is 34. Taking one number as $\displaystyle x$ from an equation in $\displaystyle x$ and hence find the numbers. The numbers are:

The value of $\displaystyle y$ of fraction $\displaystyle \frac{x}{y}$ exceeds with $\displaystyle x$ by 5 and if 3 be added to both the fraction becomes $\displaystyle \frac{3}{2}$. Find the fraction.

If difference between a number and its positive square root is 12, the numbers are

4 tables and 3 chairs together cost $\displaystyle 2,250$ and 3 tables and 4 chairs cost $\displaystyle 1,950$. Find the cost of 2 chairs and 1 table.

The ages of two persons are in the ratio $\displaystyle 5:7$. Eighteen years ago their ages were in the ratio of $\displaystyle 8:13$, their present ages (in years) are:

A box contains $\displaystyle 56$ in the form of coins of one rupee, 50 paise and 25 paise. The number of 50 paise coin is double the number of 25 paise coins and four times the numbers of one rupee coins. The numbers of 50 paise coins in the box is

Find the positive value of $\displaystyle k$ for which the equations: $\displaystyle x^2 + kx + 64 = 0$ & $\displaystyle x^2 - 8x + k = 0$ will have real roots:

The sum of two numbers is 75 and their difference is 20. Find the difference of their squares.

A number consists of two digits. The digits in tens place is 3 times the digit in the unit's place. If 54 is subtracted from the digits are reversed. The number is

4 tables and 3 chairs, together, cost $\displaystyle 2,250$ and 3 tables and 4 chairs cost $\displaystyle 1,950$. Find the cost of 2 chairs and 1 table.

Aman walks a certain distance with certain speed. If he walks $\displaystyle \frac{1}{2}$ km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking:

If $\displaystyle 2x^2 - (a+6)x + 12a = 0$, then the roots are:

Solving equation $\displaystyle m + \frac{1}{m} = \frac{6}{25}$, the value of $\displaystyle m$ works out to:

The value of $\displaystyle p$ for which the difference between the root of equation $\displaystyle x^2 + px + 8 = 0$ is 2

If the quadratic equation $\displaystyle x^2 + px + q = 0$ and $\displaystyle x^2 + p'x + q' = 0$ have a common root then $\displaystyle p + q'$?

The harmonic mean of the roots of the equation $\displaystyle (5 + \sqrt{2})x^2 - (4 + \sqrt{5})x + 8 + 2\sqrt{5} = 0$ is

The sum of square of any real positive quantity and its reciprocal is never less than:

If one root is half of the other of a quadratic equation and the difference in roots is $\displaystyle a$, then the equation is

If $\displaystyle \alpha + \beta = -2$ and $\displaystyle \alpha\beta = -3$, then $\displaystyle \alpha, \beta$ are the roots of the equation, which is:

If $\displaystyle \alpha, \beta$ are the roots of the equation $\displaystyle x^2 + x + 5 = 0$ then $\displaystyle \frac{\alpha}{\beta} + \frac{\beta}{\alpha}$ is equal to

Let $\displaystyle \alpha$ and $\displaystyle \beta$ be the roots of $\displaystyle x^2 + 7x + 12 = 0$. Then the value of $\displaystyle (\frac{\alpha}{\beta} + \frac{\beta}{\alpha})$ will be:

When two roots of QE are $\displaystyle a, \frac{1}{a}$ then what will be the quadratic equation?

Find the condition that one roots is double the other of $\displaystyle ax^2 + bx + c = 0$

Find the value of $\displaystyle K$ in $\displaystyle 3x^2 - 2kx + 5 = 0$ if $\displaystyle x = 2$

The rational root of the equation $\displaystyle 0 = 2p^3 - p^2 - 4p + 2$ is:

If the square of a number exceeds twice of the number by $\displaystyle 15$, then number that satisfies the condition is

If the second root of the given equation is reciprocal of first root then value of 'K' in the equation $\displaystyle 5x^2 - 13x + K = 0$

If the roots of the equation $\displaystyle x^2 - px + q = 0$ are in the ratio $\displaystyle 2:3$, then:

What will be the value of $\displaystyle k$, if the roots of the equation $\displaystyle (k-4)x^2 - 2kx + (k+5) = 0$ are equal?

If $\displaystyle \alpha$ and $\displaystyle \beta$ are roots of the quadratic equation $\displaystyle x^2 - 2x - 3 = 0$ then the equation whose roots are $\displaystyle \alpha + \beta$ and $\displaystyle \alpha - \beta$ is:

If $\displaystyle \alpha$ and $\displaystyle \beta$ are roots of the equation $\displaystyle x^2 - (n^2+1)x + \frac{1}{2}(n^2+n^4+1) = 0$ then the value of $\displaystyle \alpha^2 + \beta^2$ is:

If $\displaystyle \alpha, \beta$ are the roots of the equation $\displaystyle x^2 - 4x + 1 = 0$, then value of $\displaystyle \alpha^3 + \beta^3$ will be

If $\displaystyle \alpha$ and $\displaystyle \beta$ are roots of the equation $\displaystyle ax^2 + bx + c = 0$ then the equation whose roots are $\displaystyle 1$ and $\displaystyle \frac{1}{\beta}$ is:

If $\displaystyle \alpha$ and $\displaystyle \beta$ are roots of the equation $\displaystyle x^2 - 8x + 12 = 0$ then $\displaystyle \frac{1}{\alpha} + \frac{1}{\beta} =$

The roots of the equation $\displaystyle x^2 - 7x + 10 = 0$ are:

If one of the root of the equation $\displaystyle x^2 - 3x + k = 0$ is $\displaystyle 1$ then the value of $\displaystyle k$ is

When two roots of quadratic equations are $\displaystyle \alpha$ and $\displaystyle \frac{1}{\alpha}$ then what will be quadratic equation.

If $\displaystyle \alpha$ and $\displaystyle \beta$ be the roots of the equation $\displaystyle 2x^2 - 4x - 3 = 0$ the value of $\displaystyle \alpha^2 + \beta^2$ is

If one of the root of the equation $\displaystyle x^2 + 7x + p = 0$ be reciprocal of the other, then the value of $\displaystyle p$ is_

If one root of the quadratic equation is $\displaystyle 2 + \sqrt{3}$, the equation is _____.

The roots of the quadratic equation $\displaystyle x^2 - 4x + k = 0$ are coincident if

The roots of the equation $\displaystyle x^2 + (2p-1)x + p^2 = 0$ are real if

The roots of the quadratic equation $\displaystyle 9x^2 + 3kx + 4 = 0$ are equal if

If one root of a equation is $\displaystyle 2 + \sqrt{5}$, then the quadratic equation is

If one root of the equation $\displaystyle x^2 - 3x + k = 0$ is $\displaystyle 2$, then the value of $\displaystyle k$ will be

If arithmetic mean between roots of a quadratic equation is $\displaystyle 8$ and the geometric mean between them is $\displaystyle 5$, the equation is

Roots of the equation $\displaystyle 3x^2 - 14x + k = 0$ will be reciprocal of each other if:

The equation $\displaystyle 3x^2 + mx + n = 0$ has roots that are double that of equation $\displaystyle x^2 + 10x + 12 = 0$. What is the value of $\displaystyle m + n$?

If $\displaystyle \alpha, \beta$ are the roots of equation $\displaystyle x^2 + 7x + 12 = 0$ then the equation whose roots $\displaystyle (\alpha + \beta)^2$ and $\displaystyle (\alpha - \beta)^2$ will be

The equation $\displaystyle x^2 - (p+4)x + 2p + 5 = 0$ has equal roots. The value of $\displaystyle p$ is

Let $\displaystyle \alpha, \beta$ be the roots of equation $\displaystyle x^2 + 7x + 12 = 0$ then the value of $\displaystyle \left(\frac{\alpha^2}{\beta} + \frac{\beta^2}{\alpha}\right)$ will be

Given the Quadratic Equation $\displaystyle \frac{x+1}{x-1} + \frac{x-2}{x+2} = \frac{3}{1}$.

The roots of equation $\displaystyle 9x^2 - 6.3x + 1 = 0$ are

The roots of the equation $\displaystyle x^2 - x + 1 = 0$ are

If one root of the QE is $\displaystyle 2 + \sqrt{3}$, the equation is

If $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the equation $\displaystyle x^2 + 7x + 12 = 0$, then the equation whose roots are $\displaystyle (\alpha + \beta)^2$ and $\displaystyle (\alpha - \beta)^2$ will be:

Roots of the equation $\displaystyle 2x^2 + 3x + 7 = 0$ are $\displaystyle \alpha$ and $\displaystyle \beta$ then the value of $\displaystyle \alpha^{-1} + \beta^{-1}$ is

If the ratio of the roots of the equation $\displaystyle 4x^2 - 6x + p = 0$ is $\displaystyle 1:2$, then the value of $\displaystyle p$ is:

If roots of equation $\displaystyle x^2 + x + r = 0$ are $\displaystyle \alpha$ and $\displaystyle \beta$ and $\displaystyle \alpha^3 + \beta^3 = -6$. Find the value of 'r'

If one root is $\displaystyle 5z^2 + 13z + y = 0$ is reciprocal of the other, then the value of $\displaystyle y$ is

Find value of $\displaystyle x^2 - 10x + 1$, if $\displaystyle x = \frac{1}{5 - 2\sqrt{6}}$

Find the value of $\displaystyle k$ in $\displaystyle 3x^2 - 2kx + 5 = 0$ if $\displaystyle x = 2$.

If one root of the quadratic equation is $\displaystyle 2 - \sqrt{3}$ from the equation, except that the roots are irrational. Then find the Quadratic equation.

If the roots of $\displaystyle (K-4)x^2 - 2Kx + (K+5) = 0$ are coincident. Then the value of $\displaystyle K$?

If $\displaystyle x = 3^{1/3} + 3^{-1/3}$ and $\displaystyle y = 3^{1/3} - 3^{-1/3}$ then the value $\displaystyle (3x^2 + y^2)^2$ will be

If arithmetic mean between roots of a quadratic equation is $\displaystyle 8$ and the geometric mean between them is $\displaystyle 5$, the equation is _______.

The value of $\displaystyle \sqrt{6 + \sqrt{6 + \sqrt{6 + ...... \infty}}}$

One root of the eq. $\displaystyle x^2 - (2 + 5m)x + 3(7 + m) = 0$ is reciprocal of the other. Find the value of $\displaystyle m$.

The equation $\displaystyle x^2 - (p + 4)x + 2p + 5 = 0$ has equal roots. The value of $\displaystyle p$ is

If $\displaystyle \alpha$ and $\displaystyle \beta$ are roots of the equation $\displaystyle x^2 - 8x + 12 = 0$ then $\displaystyle 1/\alpha + 1/\beta =$

If $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the equation $\displaystyle x^2 + 7x + 12 = 0$, then the equation whose roots $\displaystyle (\alpha + \beta)^2$ and $\displaystyle (\alpha - \beta)^2$ will be:

Roots of the quadratic equation $\displaystyle x^3 + 9x^2 - x - 9 = 0$.

The value of 'k' is ______, if $\displaystyle 2$ is the root of the following cubic equation: $\displaystyle x^3 - (k+1)x + k = 0$

Solve $\displaystyle x^3 - 7x + 6 = 0$

The sol. of cubic eq. $\displaystyle x^3 - 23x^2 + 142x - 120 = 0$ is given by the triplet:

The roots of the equation $\displaystyle x^3 + x^2 - x - 1 = 0$ are

The equation $\displaystyle x^3 - 3x^2 - 4x + 12 = 0$ has three real roots. They are:

If one of the root of the cubic equation $\displaystyle 3x^3 - 5x^2 - 11x - 3 = 0$ is $\displaystyle \frac{1}{3}$, then other two roots are:

The equation $\displaystyle x^3 - 3x^2 - 4x + 12 = 0$ has three real roots, they are:

If $\displaystyle x = 5^{1/3} + 5^{-1/3}$, then $\displaystyle 5x^3 - 15x$ is given by

$\displaystyle (x+4)$ is a factor of $\displaystyle x^3 + 4x^2 - x - bx + 24$. Also, $\displaystyle a+b = 29$. Find the value of $\displaystyle b$.

Roots of the equation $\displaystyle x^3 + 2x^2 - x - 2 = 0$:

The roots of the cubic eq. $\displaystyle x^3 - 7x + 6 = 0$ are:

If ₹ 58 is divided among 150 children such that each girl and each boy gets 25 p and 50 p respectively. Then how many girls are there?

Puru gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Ishu gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?

The quadratic equation $\displaystyle 2x^2 - \sqrt{5}x + 1 = 0$ has

For equation $\displaystyle x^3 - 6x^2 + 5x + 12 = 0$, the product of two roots is 12. Which of the following is correct set of roots of the equation?

If $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the equation $\displaystyle x^2-x-6=0$, then the value of $\displaystyle \alpha^3+\beta^3+\alpha^2+\beta^2+\alpha+\beta$ is equal to

The roots of the equation $\displaystyle \left(\frac{x}{x-1}\right)^2 - 5\left(\frac{x}{x-1}\right) + 6 = 0$ are:

If $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the equation $\displaystyle 2x^2-6x+3=0$, then the equation with the roots $\displaystyle \frac{\alpha}{\beta}$ and $\displaystyle \frac{\beta}{\alpha}$ is

If $\displaystyle 2x + 3y = 34$ and $\displaystyle \frac{x+y}{y} = \frac{13}{8}$, find the value of $\displaystyle 7x + 5y$.

The value of is $\displaystyle \sqrt{5+\sqrt{5+\sqrt{5+\dots\infty}}}$ is

If $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the equation $\displaystyle 2x^2 -3x + 1 = 0$ then the equation whose roots are $\displaystyle 1/\alpha$ and $\displaystyle 1/\beta$ is:

One year ago, the ratio of ages (in years) of A and B was 5:4. The ratio of their ages, 4 years from now, will be 6:5. What will be the age of A (in years) after 10 years from now?

If $\displaystyle \alpha, \beta$ are the roots of equation $\displaystyle x^2 - 4x + 5 = 0$ then the equation having roots $\displaystyle \frac{1}{\alpha}$ & $\displaystyle \frac{1}{\beta}$ is

If $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the equation $\displaystyle 2x^2 + 5x + k = 0$, and $\displaystyle 4(\alpha^2 + \beta^2) + \alpha\beta = 23$, then which of the following is true?

If the ratio of the roots of the Equation $\displaystyle 4x^2 - 6x + p = 0$ is $\displaystyle 1:2$. Then the value of $\displaystyle p$ is:

If $\displaystyle \alpha, \beta$ are the roots of the QE $\displaystyle 3x^2 - 4x + 1 = 0$, the eq. having roots $\displaystyle \frac{\alpha^2}{\beta}$ and $\displaystyle \frac{\beta^2}{\alpha}$ is:

If ₹ 58 is divided among 150 children such that each girl and each boy gets 25 p and 50 p respectively. Then how many girls are there?

Puru gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Ishu gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?

The quadratic equation $\displaystyle 2x^2 - \sqrt{5}x + 1 = 0$ has

For equation $\displaystyle x^3 - 6x^2 + 5x + 12 = 0$, the product of two roots is 12. Which of the following is correct set of roots of the equation?

If $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the equation $\displaystyle x^2-x-6=0$, then the value of $\displaystyle \alpha^3+\beta^3+\alpha^2+\beta^2+\alpha+\beta$ is equal to

The roots of the equation $\displaystyle \left(\frac{x}{x-1}\right)^2 - 5\left(\frac{x}{x-1}\right) + 6 = 0$ are:

If $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the equation $\displaystyle 2x^2-6x+3=0$, then the equation with the roots $\displaystyle \frac{\alpha}{\beta}$ and $\displaystyle \frac{\beta}{\alpha}$ is

If $\displaystyle 2x + 3y = 34$ and $\displaystyle \frac{x+y}{y} = \frac{13}{8}$, find the value of $\displaystyle 7x + 5y$.

The value of is $\displaystyle \sqrt{5+\sqrt{5+\sqrt{5+\dots\infty}}}$ is

If $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the equation $\displaystyle 2x^2 -3x + 1 = 0$ then the equation whose roots are $\displaystyle 1/\alpha$ and $\displaystyle 1/\beta$ is:

One year ago, the ratio of ages (in years) of A and B was 5:4. The ratio of their ages, 4 years from now, will be 6:5. What will be the age of A (in years) after 10 years from now?