Question

Find two consecutive even natural numbers such that the sum of their squares is 340.

Answer 1

Let first even natural number = 2x
Then second number = 2x + 2
According to the condition,
(2x)² + (2x + 2)² = 340
4x² + 4x + 8x + 4 = 340
⇒ 8x² + 8x + 4 - 340 = 0
⇒ 8x² + 8x - 336 = 0
⇒ x² + x - 42 = 0       ...(Dividing by 8)
⇒ x² + 7x - 6x - 42 = 0
⇒ x(x + 7) -6(x + 7) = 0
⇒ (x + 7)(x - 6) = 0
EIther x + 7 = 0,
then x = -7
or
x - 6 = 0,
then x = 6
∴ First even natural number = 2x 
= 2 x 6
= 12
and second 
= 12 + 2
= 14
∴ Numbers are 12, 14.