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`sqrt(x) + sqrt(x-8) = 0`
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You need to solve for x the following equation, such that:
sqrt x + sqrt (x - 8) = 0
You need to raise to square both sides, using the following formula, such that:
(a + b)^2 = a^2 + 2ab + b^2
Considering a = sqrt x, b = sqrt(x - 8) yields:
(sqrt x + sqrt (x - 8))^2 = x + 2sqrt(x(x - 8)) + x - 8 => (sqrt x + sqrt (x - 8))^2 = 0 => 2x - 8 + 2sqrt(x(x - 8)) = 0
Isolating the square root to the left side, yields:
2sqrt(x(x - 8)) = 8 - 2x
sqrt(x(x - 8)) = 4 - x
Raising to square again, yields:
(x(x - 8)) = (4 - x)^2 => x^2 - 8x = 16 - 8x + x^2
Reducing duplicate terms both sides yields:
0 = 16 invalid
Hence, evaluating the solution to the given equation yields that there are no solutions.
Posted by sciencesolve on April 11, 2013 at 7:21 PM (Answer #1)
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