SOLUTION: if the product of three consecutive positive integers is equal to their sum than what woe the sum of their squares?

Algebra.Com
Question 1085996: if the product of three consecutive positive integers is equal to their sum than what woe the sum of their squares?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

    x(x+1)(x+2) = x+(x+1)+(x+2)
     x(x²+3x+2) = x+x+1+x+2
      x³+3x²+2x = 3x+3
     x³+3x²-x-3 = 0
 x²(x+3)-1(x+3) = 0
    (x+3)(x²-1) = 0
(x+3)(x-1)(x+1) = 0

x+3=0;  x-1=0; x+1=0
  x=-3    x=1;   x=-1

The only one that's positive is x=1,

So the three consecutive integers are 1,2,3.

The sum of their squares = 1²+2²+3² = 1+4+9 = 14

Edwin
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