[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
Find x^4 + 1/x^4 if x – 1/x = 2.
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- Max@Math Revolution
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(x - 1/x)² = 2²Max@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
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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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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