Question

find the 2 positive odd consecutive integers sum of whose squares is 290

Answer 1

let the req. nos. be x and x+2
x^2 + (x+2)^2 = 290
x^2 + x^2 + 4 + 4x = 290
2x^2 +4x +4 = 290
2x^2 +4x - 286 =0
2 ( x^2 + 2x- 143 )=0
x^2 +2x - 143 = 0
x^2 + 13x - 11x -143 =0
x( x +13) - 11 ( x +13)
x= 11