Why is sqrt(x^2+x) = x•sqrt(1+1/x)?

6 Answers

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  • 1 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.

  • mizoo
    Lv 7
    1 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 s
    Lv 7
    1 year ago

    actually it is not valid.....need either x ≥ 0 or | x |√ ( 1 + 1 / x ) for x in (-∞ , -1] U [ 0 , ∞)

  • 1 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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  • 1 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.

  • 1 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.

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