Question

Find the consecutive even integers whose squares have the sum 340.

Answer 1

The even numbers are 12 and 14

Step-by-step explanation:

Given: The sum of the squares of two consecutive even number is 340.

Solution:

Let the consecutive even numbers be 2x and 2x+2.

Given that (2x)² + (2x+2)² = 340

4x² + 4x² + 4 + 8x = 340

8x² + 8x - 336 = 0

Dividing by 8, we get: x² + x - 42 = 0

x² + 7x - 6x - 42 = 0

x (x + 7) - 6 (x + 7) = 0

(x + 7) (x - 6) = 0

Therefore x = +6, -7.

Taking x = 6, the even numbers are 12 and 14.

12² + 14² = 144 + 196 = 340