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# If x-5=√x+√5 , which of followings is true?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If x-5=√x+√5 , which of followings is true?  [#permalink]

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Updated on: 20 Oct 2017, 01:12
2
8
00:00

Difficulty:

65% (hard)

Question Stats:

60% (02:49) correct 40% (03:03) wrong based on 58 sessions

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[GMAT math practice question]

If x-5=√x+√5 , which of followings is true?

A. x^2+12x+16 = 0
B. x^2-12x+16 = 0
C. x^2+6x+8 = 0
D. x^2-6x+8 = 0
E. x^2+6x-8 = 0

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"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" Originally posted by MathRevolution on 18 Oct 2017, 03:23. Last edited by MathRevolution on 20 Oct 2017, 01:12, edited 1 time in total. Retired Moderator Joined: 25 Feb 2013 Posts: 1158 Location: India GPA: 3.82 Re: If x-5=√x+√5 , which of followings is true? [#permalink] ### Show Tags 18 Oct 2017, 06:02 1 MathRevolution wrote: [GMAT math practice question] If x-5=√x+√5 , which of followings is true? A. x^2+12x+16 = 0 B. x^2-12x+16 = 0 C. x^2+6x+8 = 0 D. x^2-6x+8 = 0 E. x^2+6x-8 = 0 $$(\sqrt{x})^2-(\sqrt{5})^2=\sqrt{x}+\sqrt{5}$$ $$(\sqrt{x}+\sqrt{5})(\sqrt{x}-\sqrt{5})=(\sqrt{x}+\sqrt{5})$$ $$\sqrt{x}-\sqrt{5}=1$$ ($$\sqrt{x}+\sqrt{5}>0$$, so it can be divided from both sides) $$\sqrt{x}=1+\sqrt{5}$$, square both sides to get $$x=6+2\sqrt{5} =>x-6=2\sqrt{5}$$, again square both sides and solve it to get $$x^2-12x+16=0$$ Option B Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8261 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x-5=√x+√5 , which of followings is true? [#permalink] ### Show Tags 20 Oct 2017, 01:11 => x-5=√x+√5 is equivalent to (√x+√5)(√x-√5)=√x+√5 or √x+√5=1 √x=√5 + 1 x = 5 + 2√5 + 1 = 6 + 2√5 (x-6)^2 = 20 x^2 – 12x + 36 = 20 x^2 – 12x + 16 = 0 Therefore, the answer is B. Answer: B _________________ 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"
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Re: If x-5=√x+√5 , which of followings is true?  [#permalink]

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05 Jun 2019, 01:59
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Re: If x-5=√x+√5 , which of followings is true?   [#permalink] 05 Jun 2019, 01:59
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