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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 ## If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? tagged by: fskilnik@GMATH ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 3) If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? (A) 7.75 (B) 10 (C) 12.25 (D) 15 (E) 20 Answer: _____(E)__ _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15344 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 fskilnik@GMATH wrote: [size=17]GMATH practice exercise (Quant Class 3) If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? (A) 7.75 (B) 10 (C) 12.25 (D) 15 (E) 20 (r + 1/r)Â² = 5 r + 1/r = âˆš5 (r + 1/r)Â² = 5 rÂ² + 1/rÂ² + 2(r)(1/r) = 5 rÂ² + 1/rÂ² + 2 = 5 rÂ² + 1/rÂ² = 3 Multiplying the blue equation and the red equation, we get: (rÂ² + 1/rÂ²)(r + 1/r) = 3âˆš5 rÂ³ + (rÂ²)(1/r) + (1/rÂ²)(r) + 1/rÂ³ = 3âˆš5 rÂ³ + (r + 1/r) + 1/rÂ³ = 3âˆš5 Substituting r + 1/r = âˆš5 into the green equation above, we get: rÂ³ + âˆš5 + 1/rÂ³ = 3âˆš5 rÂ³ + 1/rÂ³ = 2âˆš5 (rÂ³ + 1/rÂ³)Â² = (2âˆš5)Â² (rÂ³ + 1/rÂ³)Â² = 20 The correct answer is E. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 3) If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? (A) 7.75 (B) 10 (C) 12.25 (D) 15 (E) 20 $${\left( {r + {1 \over r}} \right)^2} = 5\,\,\,\,\,\left( * \right)$$ $$? = {\left( {{r^3} + {1 \over {{r^3}}}} \right)^2}$$ $$?\,\,\, = \,\,\,{\left[ {\left( {r + {1 \over r}} \right)\left( {{r^2} - r \cdot {1 \over r} + {1 \over {{r^2}}}} \right)} \right]^{\,2}} = {\left( {r + {1 \over r}} \right)^2}{\left( {{r^2} - 1 + {1 \over {{r^2}}}} \right)^2}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,5 \cdot {\left( {{r^2} - 1 + {1 \over {{r^2}}}} \right)^2}\,\,\,\mathop = \limits^{\left( {**} \right)} \,\,\,20$$ $$\left( {**} \right)\,\,{r^2} - 1 + {1 \over {{r^2}}} = \left( {{r^2} + 2 + {1 \over {{r^2}}}} \right) - 3 = {\left( {r + {1 \over r}} \right)^2} - 3\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,2$$ The correct answer is (E). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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