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# If x>0 and √5x = √3x+1, what is the value of 4x^2?

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Math Expert
Joined: 02 Sep 2009
Posts: 51223
If x>0 and √5x = √3x+1, what is the value of 4x^2?  [#permalink]

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06 Jun 2017, 09:18
1
3
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:19) correct 45% (02:02) wrong based on 76 sessions

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If x>0 and $$\sqrt{5x} = \sqrt{3x}+1$$, what is the value of $$4x^2$$?

A. 1/2

B. 1

C. 4x−1

D. 10x−1

E. 16x−1

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Intern
Joined: 10 Mar 2017
Posts: 6
Location: India
Re: If x>0 and √5x = √3x+1, what is the value of 4x^2?  [#permalink]

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06 Jun 2017, 10:41
1
$$\sqrt{5x}$$ = $$\sqrt{3x}$$ +1

Squaring both the sides we get :

5x = 3x + 1 +2$$\sqrt{3x}$$

2x-1 = 2$$\sqrt{3x}$$

Squaring both sides

$$4x^2$$ + 1 -4x = 12x

$$4x^2$$ = 16x-1 Hence the answer E
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Joined: 09 Sep 2013
Posts: 9182
Re: If x>0 and √5x = √3x+1, what is the value of 4x^2?  [#permalink]

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03 Oct 2018, 04:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x>0 and √5x = √3x+1, what is the value of 4x^2? &nbs [#permalink] 03 Oct 2018, 04:40
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