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2 October, 20:45

The sum of the square of two consecutive whole number is 25. Find the numbers

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  1. 2 October, 23:30
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    Don't you mean "the sum of the squares ... "?

    The sum of the squares of two consecutive whole numbers is 25. Find the numbers. Let the first be represented by x and the second by x+1.

    Then x^2 + (x+1) ^2=25. Expanding, x^2+x^2+2x+1=25.

    Rewriting this as a quadratic equation in standard form,

    2x^2+2x+1=25, or 2x^2+2x-24=0. Simplifying, x^2+x-12=0.

    Factoring, (x-3) (x+4) = 0. Solving for x: x-3=0, so x=3; x+4=0, so x=-4.

    Choose the positive x value: x=3. Then the next consecutive number is 2+1=3+1=4.

    Check: Does 3^2 + 4^2 = 5^2 = 25? Yes.

    The numbers are 3 and 4.
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