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Math Help - Complete the Square

  1. #1
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    Complete the Square

    Any ideas on how to accomplish completing this square: x^2+y^2+z^2-xy-xz-yz=0. I've tried a few things, but I keep getting additional terms. Thanks.
    Last edited by brucewayne; September 10th 2012 at 05:17 PM.
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  2. #2
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    Re: Complete the Square

    Hello, brucewayne!

    Any ideas on how to complete this square? . x^2+y^2+z^2-xy-yz-xz\:=\:0

    \text{Multiply by 2: }\:2x^2 + 2y^2 + 2z^2 - 2xy - 2yz - 2xz \:=\:0

    . . (x^2 - 2xy + y^2) + (y^2 - 2yz + z^2) + (x^2 - 2xz + z^2) \:=\:0

    . . . . . . . . (x-y)^2 + (y-z)^2 + (x-z)^2 \:=\:0


    \text{We have: \:the sum of three squares equals zero.}

    \text{This is true when: }\:x \,=\,y\,=\,z

    Thanks from topsquark
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  3. #3
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    Re: Complete the Square

    That was quick. Muchas gracias.
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