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  1. #1
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    Maths Question

    I'm having trouble working out this question. Could someone please provide working on how to solve this.

    If 2x = a + b + c, show that (x-a)^2 + (x-b)^2 + (x-c)^2 + x^2 = a^2 + b^2 + c^2
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  2. #2
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    Quote Originally Posted by acevipa View Post
    I'm having trouble working out this question. Could someone please provide working on how to solve this.

    If 2x = a + b + c, show that (x-a)^2 + (x-b)^2 + (x-c)^2 + x^2 = a^2 + b^2 + c^2
    There are elegant ways and brutal ways ......

    Brutal:

    1. Sub x = \frac{a}{2} + \frac{b}{2} + \frac{c}{2} into (x-a)^2 + (x-b)^2 + (x-c)^2 + x^2.

    2. Expand the above.

    3. Simplify the above.
    Last edited by mr fantastic; February 4th 2008 at 12:21 AM.
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  3. #3
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    Quote Originally Posted by acevipa View Post
    I'm having trouble working out this question. Could someone please provide working on how to solve this.

    If 2x = a + b + c, show that (x-a)^2 + (x-b)^2 + (x-c)^2 + x^2 = a^2 + b^2 + c^2
    And elegant:

    (x-a)^2 + (x-b)^2 + (x-c)^2 + x^2 = x^2 - 2ax + a^2 + x^2 - 2bx + b^2 + x^2 - 2cx + c^2 + x^2

    = a^2 + b^2 + c^2 + 4x^2 -2x(a + b + c).

    Substitute a + b + c = 2x:

    = a^2 + b^2 + c^2 + 4x^2 -4x^2 = a^2 + b^2 + c^2 .


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