T asked in Science & MathematicsMathematics · 2 weeks ago

Find two consecutive odd integers such that the sum of their squares is 650?

12 Answers

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  • 2 weeks ago

    Let 2n-1 and 2n+1 be the integers.

    (2n-1)^2+(2n+1)^2 = 650

    4n^2-4n+1+4n^2+4n+1=650

    8n^2+2=650

    8n^2=648

    n^2=81

    n= +/-9

    If n=9 2n-1=17 and 2n+1=19

    If n=-9 2n-1=-19 and 2n+1=-17

    The numbers are 17 and 19 or -19 and -17.

  • Como
    Lv 7
    2 weeks ago

    :-

    ( 2n + 1 )² + ( 2n + 3 )² = 650

    4n² + 4n + 1 + 4n² + 12n + 9 = 650

    8n² + 16 n - 640 = 0

    n² + 2n - 80 = 0

    ( n + 10 ) ( n - 8 ) = 0

    n = - 10 , n = 8

    One answer is 17 , 19

  • David
    Lv 7
    2 weeks ago

    The numbers requied are 17 and 19

  • 2 weeks ago

    A=B+2,  A^2+B^2=650

    A=-17 B=-19

    A=19, B=17

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  • JOHN
    Lv 7
    2 weeks ago

    2n – 1, 2n + 1 are consecutive odd integers.

    (2n – 1)² +  (2n + 1)²

    = 8n² + 2 = 650

    8n² = 648

    n² = 81

    n = ± 9

    The numbers are (17, 19) and (-19, -17).

  • 2 weeks ago

    To make this simpler to solve, let's focus on the even integer that is between. Call this x.

    Let x-1 be the odd integer immediately before.

    Let x+1 be the odd integer immediately after.

    The sum of their squares is 650:

    (x - 1)² + (x + 1)² = 650

    x² - 2x + 1 + x² + 2x + 1 = 650

    2x² + 2 = 650

    2x² = 648

    x² = 324

    x = ±√324

    x = ±18

    So the even number between is either -18 or 18.

    There are two possible answers:

    -19 and -17

    or

    17 and 19

  • 2 weeks ago

    Half of 650 is 325, so the numbers should be near 18 (the square root of 324).

    17^2 + 19^2 = 289 + 361 = 650.

    No need to hunt any farther.

  • 2 weeks ago

    Two consecutive odd integers such that the sum of their squares is 650:

    x^2 + (x + 2)^2 - 650 = 0

    2x^2 + 4x - 646 = 0

    x^2 + 2x - 323 = 0

    Factorization: 

    (x + 19)(x − 17) = 0

    Answers:

    17 and 19 & -17 and -19.

  • 2 weeks ago

    n^2+(n+2)^2 = 650

    2n^2+4n+4=650

    2n^+4n-646=0

    n=17=> 17 and 19

  • x^2 + (x + 2)^2 = 650

    x^2 + x^2 + 4x + 4 = 650

    2x^2 + 4x + 4 = 650

    x^2 + 2x + 2 = 325

    x^2 + 2x + 1 = 324

    (x + 1)^2 = 324

    x + 1 = -18 , 18

    x = -1 - 18 , -1 + 18

    x = -19 , 17

    -19 and -17

    or

    17 and 19

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