Question

find two consecutive even number whose sum of the sqaure is 1060

Answer 1

Hey mate !!

Here's the answer !!

Let the two consecutive even numbers be " x " and " x + 2 "

Given - Sum of squares of two consecutive even numbers is equal to 1060.

=> ( x )² + ( x + 2 )² = 1060

= x² + ( x² + 4x + 4 ) = 1060

= x² + x² + 4x + 4 = 1060

= 2x² + 4x + 4 - 1060 = 0

= 2x² + 4x -1056 = 0

Divide by 2 throughout the equation

= x² + 2x - 528 = 0

= x² + 24x - 22x - 528 = 0

= x ( x + 24 ) - 22 ( x + 24 ) = 0

= ( x + 24 ) ( x - 22 ) = 0

=> x = 22 , - 24

Both the numbers are possible as when they are squared they become positive.

Hence if x = 22, the numbers are 22 and 24.

If x = - 24, then the numbers are - 24 and - 22.

Hope my answer helped you !!

Cheers !!