Question

Find two consecutive odd positive integers,sum of whose squares is 290.

Answer 1

Let the two consecutive odd integers be x and x + 2 (∵Consecutive odd numbers are at the difference of 2)

According to Question Sum of their Squares = x² + (x + 2)²

which is equals to 290

∴ x² + (x + 2)² = 290

x² + x² + 4x + 4 =290

2x² + 4x - 286 = 0

or x² + 2x - 143 = 0 (Divided whole equation by 2)

x² + 13x - 11x - 143 =0

x(x + 13) -11(x + 13)=0

(x - 11) (x + 13)=0

x - 11 = 0              x + 13 = 0

x = 11                   x = -13 (Neglected because numbers are positive integers)

∴Desired consecutive odd positive integers are x = 11 and x + 2 = 13.

Answer 2

Answer:

Step-by-step explanation: