Hay dos números naturales consecutivos y la suma del cuadrado de esos números es 221¿cuáles serán esos números?

Let x and x+1 be the consecutive integers.

The sum of squares is:
(x)² + (x+1)² = 221
Expand second term:
x² + x² + 2x + 1 = 221
Combine like terms:
2x² + 2x + 1 = 221
Subtract 221 from both sides to make quadratic form:
2x² + 2x - 220 = 0
Divide both sides by 2:
x² + x - 110 = 0
Factor:
(x + 11)(x - 10) = 0
x = -11 or x = 10

Answers: 10 and 11 or -10 and -11