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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 ## For which value of k does the following pair... tagged by: rolandprowess ##### This topic has 1 expert reply and 0 member replies ### Top Member ## For which value of k does the following pair... For which value of k does the following pair of equations yield a unique solution for x, such that the solution is positive? (x - k)^2 - y^2 = 8 (x + 2k)^2 + (y^2 - k^2) = 0 A) 4/root(7) B) root(7)/ 4 C) root(2) D) -4/root(7) E) None of these. The OA is D. I need help. There are too many variables. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello Vincen. From the second equation we get: (3) $$y^2-k^2=-\left(x+2k\right)^2.$$ Now, from the first equation we can get: (4) $$x^2-2kx+k^2-y^2=8\ <=>x^2-2kx-\left(y^2-k^2\right)=8.$$ Substituiting equation (3) in (4) we will get: (5) $$x^2-2kx+\left(x+2k\right)^2=8\ <=>\ x^2+kx+2k^2-4=0.$$ Now, we want that equation (5) have only one solution. It is equivalent to say that $$\triangle=0.$$ This is to say, $$k^2-4\left(2k^2-4\right)=0\ <=>\ k^2=\frac{16}{7}.$$ The last equation give us two solutions for k, $$k_1=\frac{4}{\sqrt{7}}\ and\ k_2=-\frac{4}{\sqrt{7}}.$$ Now, the solution for the equation (5) is -k/2. We want this solution would be positive, so we have to select the option 2. The value of k is $$k_2=-\frac{4}{\sqrt{7}}.$$ The correct option is D. I hope this solution will be enough clear to help you. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT 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 • Award-winning private GMAT tutoring Register now and save up to$200

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