Question

The sum of the squares of two consecutive odd natural numbers is 290 , find the numbers ?​

Answer 1

Answer:

The integers are 11, 13.

Step-by-step explanation:

Let the first integer be x. Then the second integer is x + 2.

Given that sum of squares of two consecutive integers is 290.

x^2 + (x+2)^2 = 290

x^2 + x^2 + 4x + 4 = 290

2x^2 + 4x + 4 = 290

2x^2 + 4x = 286

x^2 + 2x = 143

x^2 + 2x - 143 = 0

x^2 + 13x - 11x - 143 = 0

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

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

x = 11,-13.

If x = 11 then x + 2 = 13.

The integers are 11, 13.