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If x - 7 = √x + √7 , x = ?

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If x - 7 = √x + √7 , x = ?  [#permalink]

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New post Updated on: 21 Aug 2017, 01:55
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If \(x - 7 = √x + √7\) , x = ?

A. 8 + 2√7
B. 8 - 2√7
C. 8 + √7
D. 8 - √7
E. 7 + 2√8

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Originally posted by MathRevolution on 21 Aug 2017, 01:26.
Last edited by Bunuel on 21 Aug 2017, 01:55, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x - 7 = √x + √7 , x = ?  [#permalink]

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New post 21 Aug 2017, 01:32
1
MathRevolution wrote:
If x-7=√x+√7 , x=?

A. 8+2√7 B. 8-2√7 C. 8+√7 D. 8-√7 E. 7+2√8


\(x-7=\sqrt{x}+\sqrt{7} \implies (\sqrt{x}+\sqrt{7})(\sqrt{x}-\sqrt{7}) = \sqrt{x}+\sqrt{7} \implies (\sqrt{x}+\sqrt{7})(\sqrt{x}-\sqrt{7} -1)=0 \)
thus \(\sqrt{x}+\sqrt{7}=0\) or \(\sqrt{x}-\sqrt{7} -1=0\)
thus \(\sqrt{x}=\sqrt{7} +1 \implies x= 8+2\sqrt{7}\)

Answer A
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Re: If x - 7 = √x + √7 , x = ?  [#permalink]

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New post 23 Aug 2017, 01:21
=> x-7=√x+√7
(√x+√7 )(√x-√7)=√x+√7
√x-√7=1
√x = 1 +√7
x = (1 +√7)2 = 8 +2√7

Ans: A
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Re: If x - 7 = √x + √7 , x = ?  [#permalink]

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New post 29 Aug 2017, 02:49
MathRevolution wrote:
If \(x - 7 = √x + √7\) , x = ?

A. 8 + 2√7
B. 8 - 2√7
C. 8 + √7
D. 8 - √7
E. 7 + 2√8


\(x - 7 = √x + √7\)
\((√x + √7) (√x - √7) = √x + √7\)
\((√x - √7) = 1\)
\(\sqrt{x} = 1 + √7\)
\(x= 1+7+2\sqrt{7}\)
A
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Re: If x - 7 = √x + √7 , x = ?  [#permalink]

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New post 29 Aug 2017, 19:01
please provide in depth explanation of this please
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If x - 7 = √x + √7 , x = ?  [#permalink]

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New post 29 Aug 2017, 20:55
1
MathRevolution wrote:
If \(x - 7 = √x + √7\) , x = ?

A. 8 + 2√7
B. 8 - 2√7
C. 8 + √7
D. 8 - √7
E. 7 + 2√8


SandhyAvinash wrote:
please provide in depth explanation of this please

\((x - 7)\) can be written in \((a^2 - b^2) = (a+b)(a-b)\) format. Where; \((x - 7)\) is \((a^2 - b^2)\)

Therefore; \((x - 7) = (√x + √7)(√x - √7)\)

\(x - 7 = √x + √7\)

\((√x + √7)(√x - √7) = √x + √7\)

\((√x - √7) = \frac{(√x + √7)}{(√x + √7)}\)

\(√x - √7 = 1\)

\(√x = 1 + √7\)

Squaring both sides we get;

\((√x)^2 = (1 + √7)^2\)

\(x = 1 + 7 + 2√7\)

\(x = 8 + 2√7\)

Answer (A)...

Hope its clear now... :-)
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Re: If x - 7 = √x + √7 , x = ?  [#permalink]

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New post 29 Aug 2017, 23:37
MathRevolution wrote:
If \(x - 7 = √x + √7\) , x = ?

A. 8 + 2√7
B. 8 - 2√7
C. 8 + √7
D. 8 - √7
E. 7 + 2√8


\(x - 7 = √x + √7\)
(√x + √7)(√x - √7) = √x + √7
√x - √7 = 1
√x = 1 + √7
x = 1 + 7 + 2√7 = 8 + 2√7

Answer A
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Re: If x - 7 = √x + √7 , x = ? &nbs [#permalink] 29 Aug 2017, 23:37
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