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Two consecutive integers are squared. The sum of these squares is 1513. 

What are the integers?

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  • 2 months ago

    let the integers by 'n' & 'n+1' 

    Squaring 

    n^2 + ( n + 1)^2  = 

    n^2 + n^2 + 2n + 1  and it equals = 1513 

    2n^2 + 2n + 1 = 1513 

    2n^2 + 2n = 1512

     Factor out '2' 

    n^2 + n -756 = 0 

    This factors to 

    ( n + 28)(n - 27) = 0 

    Hence n= 27

    & n + 1 = 28 

  • 2 months ago

    Let x-1, x be the consecutive integers, then

    (x-1)^2+x^2=1513

    =>

    x=?

    You should find it out by yourself.

  • ?
    Lv 6
    2 months ago

    n² + (n + 1)² = 1513

    n² + n² +2n + 1 = 1513

    2n² + 2n -1512 = 0

    n² + n - 756 = 0

    (n + 28)(n - 27) = 0

    n = 27 or n = - 28

    ANS 27 and 28 or -27 and -28

  • 2 months ago

    n^2 + (n + 1)^2 = 1513

    n^2 + n^2 + 2n + 1 = 1513

    2n^2 + 2n + 1 = 1513

    2n^2 + 2n + 1 - 1513 = 0

    2n^2 + 2n - 1512 = 0

    n^2 + n - 756 = 0

    (n + 28)(n - 27) = 0

    n =- 28, n = 27

    the integers are- 28 and 27... 

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  • Ian H
    Lv 7
    2 months ago

    2x^2 + 2x = 1512

    x(x + 1) = 756 = 27*28

  • ?
    Lv 7
    2 months ago

    Two consecutive integers are squared. 

    The sum of these squares is 1513. 

    x^2 + (x + 1)^2 = 1513

    2x^2 + 2x - 1512 = 0

    x^2 + x - 756 = 0

    (x - 27) (x + 28) = 0The integers are 27 and 28.

  • 2 months ago

    call them x and x+1

    sum of squares is

    x² + (x+1)² = 1513

    x² + x² + 2x + 1 – 1513 = 0

    2x² + 2x – 1512 = 0

    x = 27, – 28 (using a quadratic solver)

    so the integers are 27, 28

    or –27, –28

  • Amy
    Lv 7
    2 months ago

    Consecutive integers differ by 1. If you call the smaller number x, then the other is x+1. 

    We can thus translate the statement into the equation

    x^2 + (x+1)^2 = 1513

    Expand the (x+1)^2 term, then collect like terms to make an equation of the form Ax^2 + Bx + C = 0.

    Then either factor or use the quadratic equation to solve for x.

    You will get two solutions, one positive and one negative, whose absolute values differ by 1. This is because positive and negative numbers have the same square. For example, 2^2 + 3^2 = (-2)^2 + (-3)^2

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