If P = x1/3 + x-1/3 then find value of $3P3 - 9P$

Option c: $3(x+1/x)$. Solution: We are given: P = x1/3 + x-1/3 Let us cube both sides of the equation using the algebraic identity: (u+v)3 = u3 + v3 + 3uv(u+v) Here, let u = x1/3 and v = x-1/3 . The product uv is: uv = x1/3 × x-1/3 = x1/3 - 1/3 = x0 = 1 Now, applying the identity: P3 = ( x1/3 )3 + ( x-1/3 )3 + 3(1)( x1/3 + x-1/3 ) P3 = x + x-1 + 3P P3 = x + 1/x + 3P Rearranging the terms by moving $3P to the left side: P3 - 3P = x + 1/x We need to find the value of $3P3 - 9P . Factor out 3 from the expression: 3P3 - 9P = 3( P3 - 3P ) Substituting the value of P3 - 3P : 3P3 - 9P = 3( x + 1/x ) Hence, Option C is the correct answer.

If P = x1/3 + x-1/3 then find value of $3P3 - 9P$

The correct answer is Option c: $3(x+1/x)$. We are given: P = x1/3 + x-1/3 Let us cube both sides of the equation using the algebraic identity: (u+v)3 = u3 + v3 + 3uv(u+v) Here, let u = x1/3 and v = x-1/3 . The product uv is: uv = x1/3 × x-1/3 = x1/3 - 1/3 = x0 = 1 Now, applying the identity: P3 = ( x1/3 )3 + ( x-1/3 )3 + 3(1)( x1/3 + x-1/3 ) P3 = x + x-1 + 3P P3 = x + 1/x + 3P Rearranging the terms by moving $3P to the left side: P3 - 3P = x + 1/x We need to find the value of $3P3 - 9P . Factor out 3 from the expression: 3P3 - 9P = 3( P3 - 3P ) Substituting the value of P3 - 3P : 3P3 - 9P = 3( x + 1/x ) Hence, Option C is the correct answer.

Ratio, Proportion, Indices, LogarithmMCQMTP March 22Question 909 of 302

All Questions

If $\displaystyle P = x^{1/3} + x^{-1/3}$ then find value of $3P^3 - 9P$

Select Your Answer (Keyboard: A, B, C, D)

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — $3(x+1/x)$

All Options:

A $\displaystyle 3$
B $\displaystyle 1/2(x+1/x)$
C$3(x+1/x)$
D$2(x+1/x)$

Detailed Solution & Explanation

We are given:

P = x^{1/3} + x^{-1/3}

Let us cube both sides of the equation using the algebraic identity:

(u+v)^3 = u^3 + v^3 + 3uv(u+v)

Here, let

\displaystyle u = x^{1/3}

and

\displaystyle v = x^{-1/3}

. The product

\displaystyle uv

is:

uv = x^{1/3}

Now, applying the identity:

P^3 = \left( x^{1/3} \right)^3 + \left( x^{-1/3} \right)^3 + 3(1)\left( x^{1/3} + x^{-1/3} \right)

P^3 = x + x^{-1} + 3P

P^3 = x +

Rearranging the terms by moving $3P

\displaystyle \frac{1}{x}

. Factor out

\displaystyle 3

from the expression:

3P^3 - 9P = 3\left( P^3 - 3P \right)

Substituting the value of

\displaystyle P^3 - 3P

3P^3 - 9P = 3\left( x +

Hence, **Option C** is the correct answer.

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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If P=x1/3+x−1/3\displaystyle P = x^{1/3} + x^{-1/3}P=x1/3+x−1/3 then find value of $3P^3 - 9P$