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Math Help - Equation needed to be solve for X

  1. #1
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    Equation needed to be solve for X

    If (square root of 4+x) + (square root of 10-x) = 6.
    Then solve (square root (4+x)(10-x)).

    (4+x)^(1/2) + (10-x)^(1/2) = 6.
    Then solve (4+x)(10-x)^(1/2)
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  2. #2
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    Quote Originally Posted by crystaly0x View Post
    If (square root of 4+x) + (square root of 10-x) = 6.
    Then solve (square root (4+x)(10-x)).

    (4+x)^(1/2) + (10-x)^(1/2) = 6.
    Then solve (4+x)(10-x)^(1/2)
    Let \sqrt{4 + x} = a
    \sqrt{10 - x} = b
    Therefore,
    a + b = 6
    (a + b)^2 = 36
    a^2 + 2ab + b^2 = 36
    2ab = 36 - a^2 - b^2
    2ab = 36 - (\sqrt{4 + x})^2 - (\sqrt{10-x})^2
    2ab = 36 - (4 + x) - (10 - x)
    2ab = 22
    ab = 11
    hence \sqrt{4 + x}\sqrt{10 - x} = \sqrt{(4 + x)(10 - x)} = 11
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