Question

The sum of the squares of three consecutive even number is 116. find the number

Answer 1

Let x,(x+2),(x+4)represent the three consecutive positive even integers  

Question states***

 x^2 + (x+2)^2 + (x+4)^2 = 116

Solving for x

 3x^2 + 12x + 20 = 116

3x^2 + 12x - 96 = 0

  x^2 + 4x - 32 = 0

factoring

(x + 8)(x-4)=0  Note:SUM of the inner product(8x) and the outer product(-4x) = 4x

(x + 8)=0  x = -8 is an Extraneous solution (not 'positive')

(x-4)=0    x = 4  the three consecutive positive even integers are 4,6,8