- Demiurge42Lv 71 year ago
It isn't. When x = -2, the left hand side is √2 and the right hand side is -√2. They are not equal.
- mizooLv 71 year ago
√(x^2 + x) = √(x^2 (1 + 1/x)) = |x|√(1 + 1/x)
If you don't mention the absolute value for x, the answer won't be correct.
- ted sLv 71 year ago
actually it is not valid.....need either x ≥ 0 or | x |√ ( 1 + 1 / x ) for x in (-∞ , -1] U [ 0 , ∞)
- KrishnamurthyLv 71 year ago
sqrt(x^2 + x) = x • sqrt(1 + 1/x)
(x^2 + x) = x^2•(1 + 1/x)
x^2 + x = x^2 + x
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- oldprofLv 71 year ago
Because x^2 + x = x^2 (1 + 1/x) = x^2 + x QED
Square both sides and you'll see they are equal.
- Jeff AaronLv 71 year ago
sqrt(x^2 + x)
= sqrt(x^2(x + (1/x)))
= sqrt(x^2)*sqrt(x + (1/x))
If x >= 0, that's the same as x*sqrt(x + (1/x))
That also works if x = -1.
But for other values of x, those two are NOT the same.