[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
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(x - 1/x)Â² = 2Â²Max@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

xÂ² + 1/xÂ² - 2(x)(1/x) = 4

xÂ² + 1/xÂ² - 2 = 4

xÂ² + 1/xÂ² = 6

(xÂ² + 1/xÂ²)Â² = 6Â²

xâ�´ + 1/xâ�´ + (2)(xÂ²)(1/xÂ²) = 36

xâ�´ + 1/xâ�´ + 2 = 36

xâ�´ + 1/xâ�´ = 34.

The correct answer is D.

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- Max@Math Revolution
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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

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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