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Find x^4 + 1/x^4 if x - 1/x = 2.

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Find x^4 + 1/x^4 if x - 1/x = 2.

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[Math Revolution GMAT math practice question]

Find x^4 + 1/x^4 if x - 1/x = 2.

A. 14
B. 17
C. 25
D. 34
E. 36

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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

Find x^4 + 1/x^4 if x - 1/x = 2.

A. 14
B. 17
C. 25
D. 34
E. 36
(x - 1/x)² = 2²

x² + 1/x² - 2(x)(1/x) = 4

x² + 1/x² - 2 = 4

x² + 1/x² = 6

(x² + 1/x²)² = 6²

x⁴ + 1/x⁴ + (2)(x²)(1/x²) = 36

x⁴ + 1/x⁴ + 2 = 36

x⁴ + 1/x⁴ = 34.

The correct answer is D.

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=>
Now, 2^2=(x-1/x)^2 = x^2 - 2x(1/x) + 1/x^2 = x^2 + 1/x^2 - 2.
Therefore, x^2 + 1/x^2 = 4+2=6.

Squaring both sides gives
6^2=( x^2 + 1/x^2 )^2 = x^4 + 2x^2(1/x^2) + 1/x^4 = x^4 + 1/x^4 + 2.
Thus, x^4 + 1/x^4 = 36-2=34.

Therefore, the answer is D.
Answer: D

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The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

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