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GRE Math Challenge #17 - what is the value of 2x?

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GRE Math Challenge #17 - what is the value of 2x? [#permalink]  02 Jan 2015, 05:40
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85% (01:04) correct 14% (04:11) wrong based on 7 sessions
If $$\sqrt{8x^2 +17} = 3x-2$$, what is the value of 2x? _________________________
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Re: GRE Math Challenge #17 [#permalink]  02 Jan 2015, 05:41
Expert's post
[Reveal] Spoiler: Solution

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Re: GRE Math Challenge #17 [#permalink]  13 May 2015, 10:03
Why can't be the value of 'x' be -1 or -ve ?
Sorry but i'm new to GRE.
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Re: GRE Math Challenge #17 [#permalink]  20 May 2015, 10:08
Expert's post
soumya1989 wrote:
If $$\sqrt{8x^2 +17} = 3x-2$$, what is the value of 2x? _________________________

First square both sides of the equation to get: 8x² + 17 = (3x - 2)²
Expand and simplify right side: 8x² + 17 = 9x² - 12x + 4
Rearrange to get: 0 = x² - 12x - 13
Factor to get: 0 = (x - 13)(x + 1)
So, x = 13 or x = -1

IMPORTANT: For square root equations we need to always CHECK for EXTRANEOUS roots by plugging them into the original equation.

x = 13
√[8(13²) + 17] = 3(13) - 2
Simplify to get: √[some big POSITIVE number] = 37
The important thing here is that we are finding the square root of a POSITIVE value, AND the result is also POSITIVE. PERFECT!!
As such, x = 13 is a valid solution

x = -1
√[(8)((-1)²) + 17] = 3(-1) - 2
STOP
When we evaluate the RIGHT side, we get: √[(8)((-1)²) + 17] = -5
The square root of a value cannot equal -5
So, the solution x = -1 is not valid

This means x = 13 is the only valid solution.
Since the question asks for the value of 2x, the correct answer is
[Reveal] Spoiler:
(2)(13) = 26

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Re: GRE Math Challenge #17 - what is the value of 2x? [#permalink]  02 Nov 2015, 05:54
I would have checked x=-1 first since its easier to calculate.
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Re: GRE Math Challenge #17 [#permalink]  07 Sep 2017, 07:13
GreenlightTestPrep wrote:
soumya1989 wrote:
If $$\sqrt{8x^2 +17} = 3x-2$$, what is the value of 2x? _________________________

x = -1
√[(8)((-1)²) + 17] = 3(-1) - 2
STOP
When we evaluate the RIGHT side, we get: √[(8)((-1)²) + 17] = -5
The square root of a value cannot equal -5
So, the solution x = -1 is not valid

Probably, it's me that I am tired but I cannot understand how sqrt((8)((-1)^2)+17)) could be negative. -1^2 = 1 so we get sqrt(25). Am I wrong?
Re: GRE Math Challenge #17   [#permalink] 07 Sep 2017, 07:13
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