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Math

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Two consecutive integers are squared. The sum of these squares of these squares is 545. What are the integers?

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    Fast way:
    Half of 545 = 272 must fall between two perfect sequres, namely 256 and 289, which means that the integers are 16 and 17.

    Standard way:
    Let x be one of the integers, then x+1 is the other. So that:
    x^2+(x+1)^2=545
    2x^2+2x-544=0
    x^2+x-272=0
    (x+17)(x-16)=0
    So x=16 or x=-17.
    The consecutive integers are therefore:
    16, 17, or
    -17, -16

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