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

Answer:

There's two answers.

-5, -4, and -3

3, 4, 5

Step-by-step explanation:

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