Question

Find two consecutive odd positive integers, sum of whose square is 290?
1. 11, 13
2. 5, 7
3. 13, 15
4. 7, 9

Answer 1

Correct Answer - Option 1 : 11, 13

Calculation:

Let the numbers be x and (x + 2) respectively

⇒ x² + (x + 2)² = 290

⇒ x² + x² + 4 + (2 × x × 2) = 290

⇒ 2x² + 4 + 4x = 290

⇒ 2x² + 4x = 290 – 4

⇒ 2x² + 4x = 286

⇒ x² + 2x – 143 = 0

⇒ x² + 13x – 11x – 143 = 0

⇒ x(x + 13) – 11(x + 13) = 0

⇒ (x – 11) (x + 13) = 0

⇒ x = 11, -13

The number can't be negative so value of x is 11

Second number = 11 + 2 = 13

∴ The consecutive odd integers are 11 and 13