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# Find x^4 + 1/x^4 if x – 1/x = 2.

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7603
GMAT 1: 760 Q51 V42
GPA: 3.82
Find x^4 + 1/x^4 if x – 1/x = 2.  [#permalink]

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23 Nov 2018, 00:56
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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 $$x – \frac{1}{x} = 2.$$

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

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 31 Jul 2017 Posts: 515 Location: Malaysia Schools: INSEAD Jan '19 GMAT 1: 700 Q50 V33 GPA: 3.95 WE: Consulting (Energy and Utilities) Re: Find x^4 + 1/x^4 if x – 1/x = 2. [#permalink] ### Show Tags 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 _________________ If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7603 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Find x^4 + 1/x^4 if x – 1/x = 2. [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Re: Find x^4 + 1/x^4 if x – 1/x = 2.   [#permalink] 25 Nov 2018, 18:38
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# Find x^4 + 1/x^4 if x – 1/x = 2.

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