<PRE><B>Question 849769</B>
I have looked up this question on wolfram and mathway and they both give 3,-5, but the 3 as an extraneous solution, and I cannot figure out why.
(rad of 4-x PLUS the rad of x+6) all equal to 4
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sqrt(4-x) + sqrt(x+6) = 4
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Square both sides to get:
(4-x) + (x+6) + 2sqrt[(4-x)(x+6)] = 16
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2sqrt(-x^2-2x+24) = 6
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sqrt(-x^2-2x+24) = 3
Square both sides to get:
-x^2-2x+24 = 9
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x^2 + 2x - 15 = 0
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Factor:
(x+5)(x-3) = 0
x = 3 or x = -5
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Neither is extraneous.
Cheers,
Stan H.
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