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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: 53734
If x>0 and √5x = √3x+1, what is the value of 4x^2?  [#permalink]

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06 Jun 2017, 10:18
1
3
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:27) correct 39% (02:09) wrong based on 82 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, 11:41
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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Re: If x>0 and √5x = √3x+1, what is the value of 4x^2?  [#permalink]

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03 Oct 2018, 05:40
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Re: If x>0 and √5x = √3x+1, what is the value of 4x^2?   [#permalink] 03 Oct 2018, 05:40
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