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algebra

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solve:
the square root of (x) +2= the square root of (5-x) +3

  • algebra -

    x = 4 is the answer, if you take the positive square roots. There may be other answers if you take the negative square root on one or both sides.

    I got that by trial and error, not by using algebra. The algebra got too messy.

  • algebra -

    Whatever roots exist must be between x = 0 and 5, otherwise you get imaginary numbers. As I said in a previous post, x=4 is the answer is you take postive squate roots on both sides. x=1 is also an answer, if you take the positive root of 1 on the left and the negative root of 4 on the right.

  • algebra -

    Here is the algebraic proof:
    sqrt(x) + 2 = sqrt(5-x) + 3
    sqrt(x) -1 = sqrt(5-x)
    2x = 2 sqrt(x) +4
    x = sqrt(x) + 2
    Let sqrt(x) = y, and you have a quadratic equation:
    y^2 -y +2 = (y-2)(y+1) = 0
    y = 2 or -1
    x = y^2 = 4 or 1

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