Correct Option: A

According to question ,
Let, the two consecutive odd positive integers be 2x + 1 and 2x + 3 where x is a whole number.
Now, ( 2x + 1 )² + ( 2x + 3 )² = 290
⇒ 4x² + 4x + 1 + 4x² + 12x + 9 = 290
⇒ 8x² + 16x - 280 = 0
⇒ x² + 2x - 35 = 0
⇒ ( x + 7 ) ( x - 5 ) = 0
⇒ x = 7, - 5
But, x = −7 is not possible, since −7 is not a whole number .
∴ x = 5.
We get , 2x + 1 = 2 x 5 + 1 = 11 and 2x + 3 = 2 x 5 + 3 = 13
Thus , two consecutive positive odd integers are 11 and 13 .