?
Lv 7
? asked in Science & MathematicsMathematics · 2 months ago

111^2 + 131^2 = ?

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    (121 - 10)^2 + (121 + 10)^2 =>

    121^2 - 2 * 121 * 10 + 10^2 + 121^2 + 2 * 121 * 10 + 10^2 =>

    2 * 121^2 + 2 * 10^2 =>

    2 * (121^2 + 10^2) =>

    2 * (14641 + 100) =>

    2 * 14741 =>

    29482

    Hey Puzzling, before you TD others, you should probably check your numbers again.

  • ?
    Lv 7
    2 months ago

    111^2 + 131^2 = 29482

    The structure of the problem suggests you may want to try some algebra on it. 

    111 = 121 - 10

    131 = 121 + 10

    a = 121 = 11^2

    b = 10

    (a-b)^2 + (a+b)^2

    = 2(a^2 + b^2)

    a^2 = 11^4 = (10+1)^4

    using the binomial theorem this is

    1*10^4 + 4*10^3 

    + 6*10^2 + 4*10 + 1

    = 14641

    Or just use Pascal’s triangle. 

    b^2 = 100

    2(14641 + 100)

    = 29282 + 200

    = 29482

    This allows you to do the problem using only mental math plus some algebra. 

  • David
    Lv 7
    2 months ago

    111 squared plus 131 squared equals 29,482

  • 2 months ago

    29,482                

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  • 2 months ago

    111² + 131²

    = 12321 + 17611

    = 29932

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