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

1.	The sum of squares of 3 consecutive no is 110 determine the number
Answer» Let three consecutive natural numbers be x, x + 1 and x +2.Then according to problem(x)2\xa0+ (x + 1)2\xa0+ (x + 2)2\xa0= 110⇒ x2\xa0+ x2\xa0+ 1 + 2x + x2\xa0+ 4 + 4x – 110 = 0⇒ 3x2\xa0+ 6x – 105 = 0⇒ x2\xa0+ 2x – 35 = 0⇒ x2\xa0+ 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 = 5But x = - 7 is rejected as it is not a natural number.Then x = 5Hence, required numbers are 5, (5 + 1), (5 + 2)i.e., 5, 6 and 7. Thanks X²+(x+1)²+(x+2)²=110. X²+x²+1+2x+x²+4+4x=110. 3x²+6x+5=110. 3x²+6x+5-1103x²+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)=0X=5,-7.The numbers are 5,6,7.

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