Question

Find two consecutive odd positive integer sum of whose square is 290.​

Answer 1

let two consecutive no. be x x+2

(x+x+2) ² = 290

x²+x²+4x+4 = 290

2x²+4x-286

2(x²+2x-143)

x²+2x-143

x²+13x-11x-143

x(x+13) -11(x+13)

x+13 =0 x = -13

x-11 = 0 x = 11

so two consecutive odd integer be 11 and 13

verification : x and x+2

(x+x+2) ² (put the value of x)

(11+11+2) ²

(11+13) ² = 121+169 = 290

hence proved...