Question

The sum of the squares of two consecutive positive even numbers in 52. Find the numbers.

Answer 1

first even number =x
second even number =x+2

\( x^2 +(x+2)^2 =52 \)

$x^2+x^2+4x+4=52$
$2\times x^2+4x-48=0$
$x^2+2x-24=0$
$(x+6)(x-4)=0$
$x=-6andx=4$

So the smaller number = 4
and the larger number is =6