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Find x^4 + 1/x^4 if x – 1/x = 2.

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by Max@Math Revolution » Thu Nov 22, 2018 11:42 pm

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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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by GMATGuruNY » Fri Nov 23, 2018 3:42 am
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

x� + 1/x� + (2)(x²)(1/x²) = 36

x� + 1/x� + 2 = 36

x� + 1/x� = 34.

The correct answer is D.
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by Max@Math Revolution » Sun Nov 25, 2018 5:26 pm
=>
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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