Find two consecutive positive integers such that the sum of their squares is 25

Discussion in 'Calculator Requests' started by math_celebrity, Jun 10, 2018.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    Find two consecutive positive integers such that the sum of their squares is 25.

    Let the first integer be x. The next consecutive positive integer is x + 1.

    The sum of their squares equals 25. We write this as::
    x^2 + (x + 1)^2

    Expanding, we get:
    x^2 + x^2 + 2x + 1 = 25

    Group like terms:
    2x^2 + 2x + 1 = 25

    Subtract 25 from each side:
    2x^2 + 2x - 24 = 0

    Simplify by dividing each side by 2:
    x^2 + x - 12 = 0

    Using our quadratic calculator, we get x = 3 or x = -4. The problem asks for positive integers, so we discard -4, and use 3.

    This means, our next positive integer is 3 + 1 = 4. So we have (3, 4) as our answers.

    Let's check our work:
    3^2 + 4^2 = 9 + 16 = 25
     

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