Question 467521
find two consecutive odd integers if the sum of their squares is 290

Let x = the smaller odd integer
  x+2 = the larger odd integer

x^2 + (x+2)^2 = 290
x^2 + x^2 + 4x + 4 = 290
2x^2 + 4x - 286 = 0

x^2 + 2x - 143 = 0

Solve by factoring
(x+13)(x-11) = 0

x-11 = 0
x = 11
x+2 = 11+2 = 13

The two consecutive odd integers are 11 and 13.