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The sum of squares of 3 …

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The sum of squares of 3 consecutive no is 110 determine the number

    • Posted by Madhavanunni Km 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 3 answers

    Gaurav Seth 6 years, 4 months ago

    Let three consecutive natural numbers be x, x + 1 and x +2.

    Then according to problem

    (x)2 + (x + 1)2 + (x + 2)2 = 110

    ⇒ x2 + x2 + 1 + 2x + x2 + 4 + 4x – 110 = 0

    ⇒  3x2 + 6x – 105 = 0

    ⇒ x2 + 2x – 35 = 0

    ⇒ x2 + 7x – 5x – 35 = 0

    ⇒ x(x + 7) – 5(x + 7) = 0

    ⇒  (x + 7)(x – 5) = 0

    ⇒ x + 7 = 0 or x – 5 = 0

    ⇒ x  = -7 or  x = 5

    But x = - 7 is rejected as it is not a natural number.

    Then x = 5

    Hence,  required numbers are 5, (5 + 1), (5 + 2)

    i.e.,  5, 6  and 7.

    1Thank You

    Madhavanunni Km 6 years, 4 months ago

    Thanks

    1Thank You

    Mayank Sharma 6 years, 4 months ago

    X²+(x+1)²+(x+2)²=110. X²+x²+1+2x+x²+4+4x=110. 3x²+6x+5=110. 3x²+6x+5-110 3x²+6x-105=o. 3(x²+2x-35). X²+2x-35=0. X²+7x-5x-35=0. X(x+7)-5(x+7). (X-5) (x+7)=0 X=5,-7. The numbers are 5,6,7.

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