Question

If the sum of squares of three consecutive numbers is 110

Answer 1

7+6+5
49+36+25
=110
7,6,5 are consecutive

Answer 2

Let the three consecutive positive integers be x, (x+1) & (x+2) ,

Then,

${x}^{2} + {(x + 1)}^{2} = {(x - 2)}^{2} = 110$

${x}^{2} + {x}^{2} + 2x + 1 + {x}^{2} + 4x + 4 = 110$

${3x}^{2} + 6x - 105 = 0$

${x}^{2} + 2x - 35 = 0$

$(x - 5)(x + 7) = 0$

$x = 5 \: or \: x = - 7$

As x is a positive integer, so x ≠ -7, so x = 5

Hence, the consecutive integers are 5,6 and 7