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

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

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New post Updated on: 20 Oct 2017, 01:12
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A
B
C
D
E

Difficulty:

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Question Stats:

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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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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.
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Re: If x-5=√x+√5 , which of followings is true?  [#permalink]

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New post 18 Oct 2017, 06:02
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
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Re: If x-5=√x+√5 , which of followings is true?  [#permalink]

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New post 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
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Re: If x-5=√x+√5 , which of followings is true? &nbs [#permalink] 20 Oct 2017, 01:11
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