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Math Help - how to solve this equation

  1. #1
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    how to solve this equation

    Solve:

    5 - √(x^2 - 7) = x - 2

    Answer key = 4

    If I square both sides, I end up with x^2 and I don't know how to get rid of the ^2.

    Please help.

    (If answer key cannot be reached, I think x^2 could be x^7 as the printing of the exponent is a superscript which is too small to read)
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  2. #2
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    Hello, shenton!

    I have the chilling feeling that you're doing it all wrong . . .


    Solve: . 5 - \sqrt{x^2-7} \:=\:x - 2

    If I square both sides, I end up with x^2 and I don't know how to get rid of the ^2.
    Two issue arise here:
    . . (1) You've never solved a quadratic before?
    . . (2) What about the radical?

    If you square both sides: . \left(5 - \sqrt{x^2 - 7}\right)^2\;=\;(x-2)^2

    . . you get: . 25 - 10\sqrt{x^2-7} + x^2 - 7 \;=\;x^2 - 4x + 4 . . . no help!


    You must isolate the radical before you square:

    . . . . . . . . . . . . . . . . 7 - x \;=\;\sqrt{x^2 - 7}


    Square: . . . . . . . . (7 - x)^2\;=\;\left(\sqrt{x^2-7}\right)^2

    and you get: . 49 - 14x + x^2\;=\;x^2 - 7

    . . . . . . . . . . . . . . . -14x \;=\;-56

    . . . . . . . . . . . . . . . . . . x \;=\;4

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  3. #3
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    Sep 2006
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    Thanks, Soroban for the help!

    I have the same chilling too, that's why I came to MHF.

    The teacher has not taught quadratic and the topic is on radicals.

    I understood your workings (thanks for the detailed workings).

    Cheers.
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