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

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed Jul 17, 2019 4:58 am

BTGmoderatorDC wrote:If \(\sqrt{3-2x} = \sqrt{2x} +1\), then \(4x^2\) =

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

OA E

Source: Official Guide

GIVEN: âˆš(3-2x) = âˆš(2x) +1

Square both sides to get: [âˆš(3-2x)]Â² = [âˆš(2x) +1]Â²

Expand and simplify to get: 3 - 2x = 2x + 2âˆš(2x) + 1

Subtract 1 from both sides to get: 1 - 2x = 2x + 2âˆš(2x)

Subtract 2x from both sides to get:2 - 4x = 2âˆš(2x)

Divide both sides by 2 to get: 1 - 2x = âˆš(2x)

Square both sides to get: (1 - 2x)Â² = [âˆš(2x)]Â²

Expand and simplify to get: 1 - 4x + 4xÂ² = 2x

Add 4x to both sides: 1 + 4xÂ² = 6x

Subtract 1 from both sides to get: 4xÂ² = 6x - 1

Answer: E

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Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by Scott@TargetTestPrep » Wed Jul 31, 2019 4:26 pm

BTGmoderatorDC wrote:If \(\sqrt{3-2x} = \sqrt{2x} +1\), then \(4x^2\) =

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

OA E

Source: Official Guide

Squaring both sides of the equation, we have:

3 - 2x = 2x + 1 + 2âˆš(2x)

2 - 4x = 2âˆš(2x)

1 - 2x = âˆš(2x)

Squaring both sides of the equation again, we have:

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

4x^2 = 6x - 1

Answer: E

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