The sum of the squares of two consecutive positive integers is 61. Find these two numbers.

Discussion in 'Calculator Requests' started by math_celebrity, Apr 25, 2017.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    The sum of the squares of two consecutive positive integers is 61. Find these two numbers.

    Let the 2 consecutive integers be x and x + 1. We have:
    x^2 + (x + 1)^2 = 61

    x^2 + x^2 + 2x + 1 = 61
    2x^2 + 2x + 1 = 61

    Subtract 61 from each side:
    2x^2 + 2x - 60 = 0

    Divide each side by 2
    x^2 + x - 30

    Using our quadratic equation calculator, we get:
    x = 5 and x = -6

    The question asks for positive integers, so we use x = 5. This means the other number is 6.

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