Question 363537: Solve the following equation and check for extraneous solutions:
Squareroot of 6 - x - square root of x - 6 = 2 Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Squareroot of 6 - x - square root of x - 6 = 2
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sqrt(6-x) - sqrt(x-6) = 2
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sqrt(6-x) = sqrt(x-6)+2
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Square both sides to get:
(6-x) = x-6 +4sqrt(x-6)+4
Simplify to get:
8-2x = 4sqrt(x-6)
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4-x = 2sqrt(x-6)
Square both sides:
16-8x+x^2 = 4(x-6)
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x^2-12x+40 = 0
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b^2 -4ac = 144 - 4*40 < 0
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So no Real Number solutions.
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Cheers,
Stan H.
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