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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If (3 - 2x)^(1/2) = (2x)^(1/2) + 1, then 4x^2 =

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Intern  B
Joined: 17 Feb 2020
Posts: 14
GMAT 1: 640 Q41 V37 GPA: 4
If (3 - 2x)^(1/2) = (2x)^(1/2) + 1, then 4x^2 =  [#permalink]

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Bunuel wrote:
SOLUTION

If $$\sqrt{3-2x} = \sqrt{2x} +1$$, then $$4x^2$$ =

(A) 1
(B) 4
(C) 2 − 2x
(D) 4x − 2
(E) 6x − 1

$$\sqrt{3-2x} = \sqrt{2x} +1$$ --> square both sides: $$(\sqrt{3-2x})^2 =(\sqrt{2x} +1)^2$$ --> $$3-2x=2x+2*\sqrt{2x}+1$$ --> rearrange so that to have root at one side: $$2-4x=2*\sqrt{2x}$$ --> reduce by 2: $$1-2x=\sqrt{2x}$$ --> square again: $$(1-2x)^2=(\sqrt{2x})^2$$ --> $$1-4x+4x^2=2x$$ --> rearrange again: $$4x^2=6x-1$$.

Thank you for the overview.

When I tackled this question the first time, I wondered whether I need to put everything what was under the radical as absolute number as I need to limit it to positive numbers only.

$$\sqrt{3-2x} = \sqrt{2x} +1$$ --> square both sides:
$$(\sqrt{3-2x})^2 =(\sqrt{2x} +1)^2$$ --> $$|3-2x|=|2x|+2*\sqrt{2x}+1$$ --

Since the math afterwards did not look funny, I dumped the question. Could someone please explain what is wrong in my logic?
Intern  B
Joined: 04 Nov 2016
Posts: 3
Re: If (3 - 2x)^(1/2) = (2x)^(1/2) + 1, then 4x^2 =  [#permalink]

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How do we know that we should use equation/algebra to solve this question? by looking at answer choices to realize that not all choices are number?
Bunuel wrote:
SOLUTION

If $$\sqrt{3-2x} = \sqrt{2x} +1$$, then $$4x^2$$ =

(A) 1
(B) 4
(C) 2 − 2x
(D) 4x − 2
(E) 6x − 1

$$\sqrt{3-2x} = \sqrt{2x} +1$$ --> square both sides: $$(\sqrt{3-2x})^2 =(\sqrt{2x} +1)^2$$ --> $$3-2x=2x+2*\sqrt{2x}+1$$ --> rearrange so that to have root at one side: $$2-4x=2*\sqrt{2x}$$ --> reduce by 2: $$1-2x=\sqrt{2x}$$ --> square again: $$(1-2x)^2=(\sqrt{2x})^2$$ --> $$1-4x+4x^2=2x$$ --> rearrange again: $$4x^2=6x-1$$. Re: If (3 - 2x)^(1/2) = (2x)^(1/2) + 1, then 4x^2 =   [#permalink] 25 Jul 2020, 08:21

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# If (3 - 2x)^(1/2) = (2x)^(1/2) + 1, then 4x^2 =  