Question

The sum
of the square of two consecutive
odd intergers is
290. Find the integers.

Answer 1

11 & 13 or - 13 & - 11

Explanation:

Let the integers are a - 1 and a + 1.

Sum of squares = 290

=> (a - 1)² + (a + 1)² = 290

=> a² + 1² - 2a + a² + 1² + 2a = 290

=> 2a² + 2 = 290

=> 2(a² + 1) = 290

=> a² + 1 = 290/2 = 145

=> a² = 145 - 1 = 144

=> a = ± √144 = ± 12

If a = + 12, numbers are

12 - 1 = 11 & 12 + 1 = 13

If a = - 12, numbers are

- 12- 1 = - 13 & - 12 + 1 = - 11