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Math Help - equations with radicals

  1. #1
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    equations with radicals

    here is the problem : 4 - √2-x = √x+6

    square each side

    (4-√2-x)^2 = (√x+6)^2

    foil and simplfy

    18-8√2-x bbbb -x = x + 6

    pretty much stuck at this point tried adding x and subtracting 18 from left side and put on right but it just turned into a diaster

    thanks!
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  2. #2
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    Quote Originally Posted by purified View Post
    here is the problem : 4 - √2-x = √x+6

    square each side

    (4-√2-x)^2 = (√x+6)^2

    foil and simplfy

    18-8√2-x bbbb -x = x + 6

    pretty much stuck at this point tried adding x and subtracting 18 from left side and put on right but it just turned into a diaster

    thanks!
    Am I correct that this is 4- \sqrtt{2-x}= \sqrt{x+ 6}?
    Then squaring gives 16- 8\sqrt{2- x}+ 2- x= x+ 6 which reduces to 18- 8\sqrt{2-x}- x= x+ 6, just as you say. Now get the square root by itself, -8\sqrt{2-x}= 2x- 12, and square both sides, 64(2- x)= 4x^2- 48x+ 144. Solve that quadratic equation for x.
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