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please explain: roots and exponents

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by talaangoshtari » Fri Jun 05, 2015 4:58 am
Hi ejager,

x+4 = √3, therefore

x-4 = √3-8
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by GMATGuruNY » Fri Jun 05, 2015 6:03 am
ejager wrote:√(x+4)² = 3
what is x-4?
By definition, √(x²) = |x|.
Equation, rephrased:
|x+4| = 3.

Case 1: Signs unchanged
x+4 = 3
x = -1.
In this case, x-4 = -1-4 = -5.

Case 2: Signs changed in the absolute value
-x-4 = 3
-7 = x.
In this case, x-4 = -7-4 = -11.
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by Brent@GMATPrepNow » Fri Jun 05, 2015 6:43 am
ejager wrote:√(x+4)² = 3
what is x-4?
As Mitch pointed out, we can rewrite the equation as |x+4| = 3

From here, we'll apply the rule: If |x| = k, then x = k or x = -k

So, we get: x+4 = 3 or x+4 = -3

1) x+4 = 3
Subtract 8 from both sides to get: x-4 = -5

2) x+4 = -3
Subtract 8 from both sides to get: x-4 = -11

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