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TAGS: GRE Instructor Joined: 10 Apr 2015
Posts: 3535
Followers: 133

Kudos [?]: 4009  , given: 65

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Expert's post 00:00

Question Stats: 48% (00:52) correct 51% (01:26) wrong based on 31 sessions
$$3x-1=\sqrt{8x^2-4x+9}$$

 Quantity A Quantity B $$x$$ $$2$$

A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com  GRE Instructor Joined: 10 Apr 2015
Posts: 3535
Followers: 133

Kudos [?]: 4009  , given: 65

2
KUDOS
Expert's post
GreenlightTestPrep wrote:
$$3x-1=\sqrt{8x^2-4x+9}$$

 Quantity A Quantity B x 2

A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Given: $$3x-1=\sqrt{8x^2-4x+9}$$

Square both sides: $$(3x-1)^2=(\sqrt{8x^2-4x+9})^2$$

Expand left side and simplify right side: $$9x^2-6x+1=8x^2-4x+9$$

Subtract $$8x^2$$ from both sides: $$x^2-6x+1=-4x+9$$

Add $$4x$$ to both sides: $$x^2-2x+1=9$$

Subtract $$9$$ from both sides: $$x^2-2x-8=0$$

Factor: $$(x-4)(x+2)=0$$

Solve: $$x=4$$ or $$x=-2$$

KEY STEP: Check for extraneous roots by testing both possible solutions.

First, plug $$x=4$$ into original equation to get: $$3(4)-1=\sqrt{8(4^2)-4(4)+9}$$
Simplify: $$11=\sqrt{121}$$
Works!
So, $$x=4$$ is a valid solution

Now plug $$x=-2$$ into original equation to get: $$3(-2)-1=\sqrt{8(-2)^2-4(-2)+9}$$
Simplify: $$-7=\sqrt{49}$$
No good! $$\sqrt{49}=7$$, not $$-7$$
So, $$x=-2$$ is an extraneous root.

Since there's only one valid solution, we get:
Quantity A: 4
Quantity B: 2

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Intern Joined: 23 Mar 2019
Posts: 27
Location: India
Followers: 0

Kudos [?]: 17 , given: 1

GreenlightTestPrep wrote:
$$3x-1=\sqrt{8x^2-4x+9}$$

 Quantity A Quantity B $$x$$ $$2$$

A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

After solving and simplifying the above-mentioned equation, we get the roots as -2 and 4.
Here, -2 is not applicable as it is not matching up with the given equation. Only 4 is matching up, which is greater than the other option.
Hence option A. Re: 3x-1=[square_root]8x^2-4x+9[/square_root]   [#permalink] 06 Sep 2019, 19:07
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