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If x - 7 = √x + √7 , x = ?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If x - 7 = √x + √7 , x = ?  [#permalink]

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Updated on: 21 Aug 2017, 01:55
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Difficulty:

55% (hard)

Question Stats:

64% (02:06) correct 36% (02:55) wrong based on 99 sessions

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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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"Only $149 for 3 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 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. Senior CR Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1354 Location: Viet Nam Re: If x - 7 = √x + √7 , x = ? [#permalink] Show Tags 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 _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7245 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x - 7 = √x + √7 , x = ? [#permalink] Show Tags 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 _________________ 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$149 for 3 month Online Course"
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Re: If x - 7 = √x + √7 , x = ?  [#permalink]

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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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29 Aug 2017, 19:01
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If x - 7 = √x + √7 , x = ?  [#permalink]

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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:

$$(x - 7)$$ 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;

$$(√x)^2 = (1 + √7)^2$$

$$x = 1 + 7 + 2√7$$

$$x = 8 + 2√7$$

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

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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

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