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Find x^4 + 1/x^4 if x – 1/x = 2.

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Math Revolution GMAT Instructor
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Find x^4 + 1/x^4 if x – 1/x = 2.  [#permalink]

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New post 23 Nov 2018, 00:56
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

55% (02:04) correct 45% (01:52) wrong based on 53 sessions

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[Math Revolution GMAT math practice question]

Find \(x^4 + \frac{1}{x^4}\) if \(x – \frac{1}{x} = 2.\)

\(A. 14\)
\(B. 17\)
\(C. 25\)
\(D. 34\)
\(E. 36\)

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Re: Find x^4 + 1/x^4 if x – 1/x = 2.  [#permalink]

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New post 23 Nov 2018, 02:24
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Find \(x^4 + \frac{1}{x^4}\) if \(x – \frac{1}{x} = 2.\)

\(A. 14\)
\(B. 17\)
\(C. 25\)
\(D. 34\)
\(E. 36\)


By Squaring on both side -

\(x^2 + \frac{1}{x^2}\) = 6

Again by squaring on both side -

\(x^4 + \frac{1}{x^4}\) = 34
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Math Revolution GMAT Instructor
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Re: Find x^4 + 1/x^4 if x – 1/x = 2.  [#permalink]

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New post 25 Nov 2018, 18:38
=>
Now, \(2^2=(x-\frac{1}{x})^2 = x^2 - 2x(\frac{1}{x}) + \frac{1}{x^2} = x^2 + \frac{1}{x^2} – 2.\)
Therefore, \(x^2 + \frac{1}{x^2} = 4+2=6.\)

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

Therefore, the answer is D.
Answer: D
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Re: Find x^4 + 1/x^4 if x – 1/x = 2.   [#permalink] 25 Nov 2018, 18:38
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