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If x2=x+2 , x=?
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Updated on: 12 Jul 2017, 19:57
Question Stats:
56% (02:09) correct 44% (02:19) wrong based on 94 sessions
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If \(x2=\sqrt{x}+\sqrt{2}\) , x=? A. \(3+2\sqrt{2}\) B. \(32\sqrt{2}\) C. \(3+\sqrt{2}\) D. \(3\sqrt{2}\) E. \(2+2\sqrt{3}\) Original Version wrote: If \(x2=\sqrt{x}+\sqrt{2}\) , x=? A. \(3+2\sqrt{2}\) B. \(32\sqrt{2}\) C. \(3+\sqrt{2}\) D. \(3\sqrt{2}\) E. \(2+2[fraction]3[/fraction]\)
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Originally posted by MathRevolution on 12 Jul 2017, 01:06.
Last edited by broall on 12 Jul 2017, 19:57, edited 2 times in total.
Fixed typo




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Re: If x2=x+2 , x=?
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12 Jul 2017, 05:47
MathRevolution wrote: If \(x2=\sqrt{x}+\sqrt{2}\) , x=? A. \(3+2\sqrt{2}\) B. \(32\sqrt{2}\) C. \(3+\sqrt{2}\) D. \(3\sqrt{2}\) E. \(2+2[fraction]3[/fraction]\) \(x2=\sqrt{x}+\sqrt{2}\) \((\sqrt{x}\sqrt{2} )(\sqrt{x}+\sqrt{2}) = (\sqrt{x}+\sqrt{2})\) \(\sqrt{x}\sqrt{2}1 = 0\) \(\sqrt{x} = 1+\sqrt{2}\) \(x = 3 +2\sqrt{2}\) Answer A
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Re: If x2=x+2 , x=?
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12 Jul 2017, 01:55
MathRevolutionThis is how I started solving this question but don't know how to solve it further.. xsq.root x= 2+sq.root 2 Squaring both the sides x^2+ x 2x*sq.root x= 2+4+4*sq.root 2 x^2x*sq.root x= 6+4* sq.root 2 x(x sq.root x)= 2(3+2* sq.root 2) Please help.
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Re: If x2=x+2 , x=?
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12 Jul 2017, 02:24
MathRevolution wrote: If \(x2=\sqrt{x}+\sqrt{2}\) , x=? A. \(3+2\sqrt{2}\) B. \(32\sqrt{2}\) C. \(3+\sqrt{2}\) D. \(3\sqrt{2}\) E. \(2+2[fraction]3[/fraction]\) MathRevolutionPlease correct the formatting for Option E. if you meant it to be \(2+2\sqrt{3}\) As for the solution : Since \(x2=\sqrt{x}+\sqrt{2}\), 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!
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Re: If x2=x+2 , x=?
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12 Jul 2017, 03:32
Solution given by pushpitkc is the best approach.
It can also be solved by plugin
\(X=3+2(2)ˆ1/2\)
\(3+2(2)ˆ1/22=(3+2(2)ˆ1/2)ˆ1/2+(2)ˆ1/2\)
\(1+2(2)ˆ1/2(2)ˆ1/2=(3+2(2)ˆ1/2)ˆ1/2\)
\((1+(2)ˆ1/2)ˆ2=3+2(2)ˆ1/2\)Squaring both the sides
\((1)ˆ2+2(2)ˆ1/2+2=3+2(2)ˆ1/2\) \(3+2(2)ˆ1/2=3+2(2)ˆ1/2\)



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Re: If x2=x+2 , x=?
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12 Jul 2017, 05:07
pushpitkc wrote: MathRevolution wrote: If \(x2=\sqrt{x}+\sqrt{2}\) , x=? A. \(3+2\sqrt{2}\) B. \(32\sqrt{2}\) C. \(3+\sqrt{2}\) D. \(3\sqrt{2}\) E. \(2+2[fraction]3[/fraction]\) MathRevolutionPlease correct the formatting for Option E. if you meant it to be \(2+2\sqrt{3}\) As for the solution : Since \(x2=\sqrt{x}+\sqrt{2}\), 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



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Re: If x2=x+2 , x=?
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12 Jul 2017, 06:55
MathRevolution wrote: If \(x2=\sqrt{x}+\sqrt{2}\) , x=? A. \(3+2\sqrt{2}\) B. \(32\sqrt{2}\) 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)*(ab). As pointed out in previous post. Good question Thanks for posting.



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Re: If x2=x+2 , x=?
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14 Jul 2017, 00:05
==> You get x2=√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
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Re: If x2=x+2 , x=?
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16 Jul 2017, 01:38
x2 = √x+√2 Use conjugate for √x+√2 = √x√2
x2 = (√x+√2) (√x√2)/(√x√2)
x2 = (x2)/(√x√2)
√x√2 = 1
√x = 1+√2
x = (1+√2)^2
x = 3+2√2  Option A



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Re: If x2=x+2 , x=?
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22 Dec 2018, 01:18
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