Question

The sum of the squares of the largest and smallest of three consecutive odd integers is 353 less than 3 times the square of the middle one. Find the integers.

Answer 1

three consecutive odds:
x-2 , x, x+2

(x-2)^2 + (x+2)^ = 3x^2 - 353
x^2 - 4x + 4 + x^2 + 4x + 4 = 3x^2 - 353
x^2 = 361
x = ±√361
x = ± 19

So the integers are:
17, 19, and 21
or
-17, -19, -21

Answer 2

Find three consecutive integers such that the product of the two largest is 29 more than the square of the smallest integer. (Enter your answers as a comma-separated list.)