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# If x-2=x+2 , x=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7603
GMAT 1: 760 Q51 V42
GPA: 3.82

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Updated on: 12 Jul 2017, 20:57
1
12
00:00

Difficulty:

65% (hard)

Question Stats:

60% (01:55) correct 40% (02:53) wrong based on 117 sessions

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If $$x-2=\sqrt{x}+\sqrt{2}$$ , x=?

A. $$3+2\sqrt{2}$$
B. $$3-2\sqrt{2}$$
C. $$3+\sqrt{2}$$
D. $$3-\sqrt{2}$$
E. $$2+2\sqrt{3}$$

Original Version wrote:
If $$x-2=\sqrt{x}+\sqrt{2}$$ , x=?

A. $$3+2\sqrt{2}$$
B. $$3-2\sqrt{2}$$
C. $$3+\sqrt{2}$$
D. $$3-\sqrt{2}$$
E. $$2+2[fraction]3[/fraction]$$

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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" Originally posted by MathRevolution on 12 Jul 2017, 02:06. Last edited by broall on 12 Jul 2017, 20:57, edited 2 times in total. Fixed typo ##### Most Helpful Community Reply Director Affiliations: IIT Dhanbad Joined: 13 Mar 2017 Posts: 731 Location: India Concentration: General Management, Entrepreneurship GPA: 3.8 WE: Engineering (Energy and Utilities) Re: If x-2=x+2 , x=? [#permalink] ### Show Tags 12 Jul 2017, 06:47 9 3 MathRevolution wrote: If $$x-2=\sqrt{x}+\sqrt{2}$$ , x=? A. $$3+2\sqrt{2}$$ B. $$3-2\sqrt{2}$$ C. $$3+\sqrt{2}$$ D. $$3-\sqrt{2}$$ E. $$2+2[fraction]3[/fraction]$$ $$x-2=\sqrt{x}+\sqrt{2}$$ $$(\sqrt{x}-\sqrt{2} )(\sqrt{x}+\sqrt{2}) = (\sqrt{x}+\sqrt{2})$$ $$\sqrt{x}-\sqrt{2}-1 = 0$$ $$\sqrt{x} = 1+\sqrt{2}$$ $$x = 3 +2\sqrt{2}$$ Answer A _________________ CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler UPSC Aspirants : Get my app UPSC Important News Reader from Play store. MBA Social Network : WebMaggu Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish". ##### General Discussion Director Joined: 02 Sep 2016 Posts: 657 Re: If x-2=x+2 , x=? [#permalink] ### Show Tags 12 Jul 2017, 02:55 MathRevolution This is how I started solving this question but don't know how to solve it further.. x-sq.root x= 2+sq.root 2 Squaring both the sides x^2+ x- 2x*sq.root x= 2+4+4*sq.root 2 x^2-x*sq.root x= 6+4* sq.root 2 x(x- sq.root x)= 2(3+2* sq.root 2) Please help. _________________ Help me make my explanation better by providing a logical feedback. If you liked the post, HIT KUDOS !! Don't quit.............Do it. Senior PS Moderator Joined: 26 Feb 2016 Posts: 3360 Location: India GPA: 3.12 Re: If x-2=x+2 , x=? [#permalink] ### Show Tags 12 Jul 2017, 03:24 1 MathRevolution wrote: If $$x-2=\sqrt{x}+\sqrt{2}$$ , x=? A. $$3+2\sqrt{2}$$ B. $$3-2\sqrt{2}$$ C. $$3+\sqrt{2}$$ D. $$3-\sqrt{2}$$ E. $$2+2[fraction]3[/fraction]$$ MathRevolution Please correct the formatting for Option E. if you meant it to be $$2+2\sqrt{3}$$ As for the solution : Since $$x-2=\sqrt{x}+\sqrt{2}$$, we can rewrite the statement to be $$x - \sqrt{x} = 2 + \sqrt{2}$$ Because $$\sqrt{2}$$ = 1.4(approximately) , the value of $$x - \sqrt{x}$$ = 2 + $$\sqrt{2}$$ = 2 +1.4 = 3.4 Using answer options, Option A, if x = $$3+2\sqrt{2}$$, the value of x = 3 + 2*1.4 = 3 + 2.8 = 5.8 Now using this value of x in the expression $$x - \sqrt{x}$$, $$x - \sqrt{x} = 5.8 - \sqrt{5.8} = 5.8 - 2.4 = 3.4$$ because $$2.4^2 = 5.76$$ which is closest to 5.8 Hence, making Option A our correct answer! _________________ You've got what it takes, but it will take everything you've got Manager Joined: 04 May 2014 Posts: 158 Location: India WE: Sales (Mutual Funds and Brokerage) Re: If x-2=x+2 , x=? [#permalink] ### Show Tags 12 Jul 2017, 04:32 Solution given by pushpitkc is the best approach. It can also be solved by plugin $$X=3+2(2)ˆ1/2$$ $$3+2(2)ˆ1/2-2=(3+2(2)ˆ1/2)ˆ1/2+(2)ˆ1/2$$ $$1+2(2)ˆ1/2-(2)ˆ1/2=(3+2(2)ˆ1/2)ˆ1/2$$ $$(1+(2)ˆ1/2)ˆ2=3+2(2)ˆ1/2$$-Squaring both the sides $$(1)ˆ2+2(2)ˆ1/2+2=3+2(2)ˆ1/2$$ $$3+2(2)ˆ1/2=3+2(2)ˆ1/2$$ Director Joined: 02 Sep 2016 Posts: 657 Re: If x-2=x+2 , x=? [#permalink] ### Show Tags 12 Jul 2017, 06:07 pushpitkc wrote: MathRevolution wrote: If $$x-2=\sqrt{x}+\sqrt{2}$$ , x=? A. $$3+2\sqrt{2}$$ B. $$3-2\sqrt{2}$$ C. $$3+\sqrt{2}$$ D. $$3-\sqrt{2}$$ E. $$2+2[fraction]3[/fraction]$$ MathRevolution Please correct the formatting for Option E. if you meant it to be $$2+2\sqrt{3}$$ As for the solution : Since $$x-2=\sqrt{x}+\sqrt{2}$$, we can rewrite the statement to be $$x - \sqrt{x} = 2 + \sqrt{2}$$ Because $$\sqrt{2}$$ = 1.4(approximately) , the value of $$x - \sqrt{x}$$ = 2 + $$\sqrt{2}$$ = 2 +1.4 = 3.4 Using answer options, Option A, if x = $$3+2\sqrt{2}$$, the value of x = 3 + 2*1.4 = 3 + 2.8 = 5.8 Now using this value of x in the expression $$x - \sqrt{x}$$, $$x - \sqrt{x} = 5.8 - \sqrt{5.8} = 5.8 - 2.4 = 3.4$$ because $$2.4^2 = 5.76$$ which is closest to 5.8 Hence, making Option A our correct answer! Great method. Squaring both the sides is a very time consuming approach. Also if there was some other value instead of sq.root 2, may be sq.root 7 or 11......How will we solve then? Should we learn the sq.roots? Thanks Intern Joined: 30 Jun 2017 Posts: 3 Re: If x-2=x+2 , x=? [#permalink] ### Show Tags 12 Jul 2017, 07:55 MathRevolution wrote: If $$x-2=\sqrt{x}+\sqrt{2}$$ , x=? A. $$3+2\sqrt{2}$$ B. $$3-2\sqrt{2}$$ C. $$3+\sqrt{2}$$ D. $$3-\sqrt{2}$$ E. $$2+2[fraction]3[/fraction]$$ I Couldn't figure out the solution at first. But, later understood that this can be solved by rewriting the LHS as (a+b)*(a-b). As pointed out in previous post. Good question- Thanks for posting. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7603 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x-2=x+2 , x=? [#permalink] ### Show Tags 14 Jul 2017, 01:05 ==> You get x-2=√x+√2 , (√x-√2)(√x+√2)= √x+√2. If you divide √x+√2 on both sides, you get √x-√2=1, then √x=√2+1. Then, if you square both sides, you get x=(√2+1)^2=2+1+2√2 =3+2√2. The answer is A. Answer: A _________________ 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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Intern
Joined: 19 Jan 2014
Posts: 35
Schools: Melbourne '20
GMAT 1: 670 Q45 V37
Re: If x-2=x+2 , x=?  [#permalink]

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16 Jul 2017, 02:38
1
x-2 = √x+√2
Use conjugate for √x+√2 = √x-√2

x-2 = (√x+√2) (√x-√2)/(√x-√2)

x-2 = (x-2)/(√x-√2)

√x-√2 = 1

√x = 1+√2

x = (1+√2)^2

x = 3+2√2 ---- Option A
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Re: If x-2=x+2 , x=?  [#permalink]

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22 Dec 2018, 02:18
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Re: If x-2=x+2 , x=?   [#permalink] 22 Dec 2018, 02:18
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