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30 June, 02:41

Sum of the squares Of two consecutive natural numbers is 313. Find the numbers.

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Answers (1)
  1. 30 June, 05:15
    0
    Set one: 12 and 13

    Set two: - 13 and - 12

    Step-by-step explanation:

    Let the smaller number = x

    Let the larger number = x + 1

    x^2 + (x + 1) ^2 = 313 Remove the brackets on the left.

    x^2 + (x^2 + 2x + 1) = 313

    x^2 + x^2 + 2x + 1 = 313 Collect like terms

    2x^2 + 2x + 1 = 313 Subtract 313 from both sides

    2x^2 + 2x + 1 - 313 = 313 - 313

    2x^2 + 2x - 312 = 0 Divide by 2

    x^2 + x - 156 = 0

    factor

    There are two sets of factors that work

    Set One

    x = 12

    x + 1 = 13

    Set Two

    x = - 13

    x+1 = - 13 + 1 = - 12

    The second set is where you will get your marks. Few people will remember to use the minus answer
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