Question

The sum of the squares of three consecutive integers is 50. Find the integers. (Hint: If one integer is x, the next consecutive positive integer is x + 1, and the third is x + 2. Simplify your answers completely. Enter your answers as a comma-separated list.)

Answer 1

There's two answers.

-5, -4, and -3

3, 4, 5

Explanation:

`x^(2) +(x+1)^(2) +(x+2)^(2) =50\\x^(2) +x^(2) +2x+1+x^(2) +4x+4=50\\3x^(2) +6x+5=50\\3x^(2) +6x-45=0\\3(x^(2) +2x-15)=0\\(x+5)(x-3)=0\\x = -5\\x = 3\\`