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 = -1IMPORTANT: 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

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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