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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Find x^4 + 1/x^4 if x - 1/x = 2. ##### This topic has expert replies Elite Legendary Member Posts: 3030 Joined: 24 Jul 2015 Location: Las Vegas, USA Thanked: 19 times Followed by:36 members ### Find x^4 + 1/x^4 if x - 1/x = 2. by Max@Math Revolution » Thu Nov 22, 2018 11:42 pm ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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 Math Revolution 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$149 for 3 month Online Course
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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)Â² = 2Â²

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.

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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. 