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1 September, 00:10

The sum of the squares of two consecutive positive integers is 41. Find the two

Positive integers.

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Answers (1)
  1. 1 September, 03:25
    0
    We have to present the number 41 as the sum of two squares of consecutive positive integers.

    1² = 1

    2² = 4

    3² = 9

    4² = 16

    5² = 25

    16 + 25 = 41

    Answer: 4 and 5

    Other method:

    n, n + 1 - two consecutive positive integers

    The equation:

    n² + (n + 1) ² = 41 use (a + b) ² = a² + 2ab + b²

    n² + n² + 2 (n) (1) + 1² = 41

    2n² + 2n + 1 = 41 subtract 41 from both sides

    2n² + 2n - 40 = 0 divide both sides by 2

    n² + n - 20 = 0

    n² + 5n - 4n - 20 = 0

    n (n + 5) - 4 (n + 5) = 0

    (n + 5) (n - 4) = 0 ↔ n + 5 = 0 ∨ n - 4 = 0

    n = - 5 0

    n = 4

    n + 1 = 4 + 1 = 5

    Answer: 4 and 5.
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