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The sum of the squares of …

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The sum of the squares of the three consecutive natural numbers is 77 . Find the numbers

    • Posted by Md Kaif 6 years, 3 months ago

    CBSE > Class 11 > Mathematics
    • 1 answers

    Rajeev Malhotra 6 years, 3 months ago

    let the three numbers are x, x+1 and x+2.

    so (x)2+(x+1)2+(x+2)2 = 77

    x2+x2+2x+1+x2+4x+4= 77

    3x2+6x+5 = 77

    3x2+6x -72 =0

    3x2+18x-12x-72 =0

    3x(x+6)-12(x+6)=0

    (3x-12)(x+6)=0

    3x-12=0 or x+6 =0

    3x=12 or x= -6

    x=12/3=4 nor x=-6

    x =4 , x=-6 is not possible because a natural number can not be negative.

    so numbers are 4,5 and 6.

     

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