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Math Help - Solving a proof

  1. #1
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    Mar 2007
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    Solving a proof

    The problem is:

    There are real numbers a and b such that

    squareroot(a+b) = squareroot(a) + squareroot(b).

    Basically, I have to find two numbers that when added together the resulting squareroot is equal to if I took the square root of each number individually and added them together. I have been trying to figure this out for hours. Teacher basically said that we just have to go through all the numbers to prove it.

    Please help!!!
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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Hello, sergeantjoker!

    Find real numbers a and b such that
    . . . _____ . . . ._ . . ._
    . . √a + b .= .√a + √b

    . . . . . . . . . . . . . . . . _____ . . . . . . _ . . . _
    Square both sides: . (√a + b) . = . (√a + √b)

    . . . . . . . . . . . . . . . . . . . . . . . .__
    And we have: . a + b . = . a + 2√ab + b

    . . . . . . . .__ . . . . . . . . .__
    Then: . 2√ab .= .0 . . √ab .= .0 . . ab .= .0


    Therefore: .either a = 0 or b = 0.

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  3. #3
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    Mar 2007
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    Thanks alot. Man, do I feel stupid now. I have been working on this problem for 2 days. Thanks again.
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