4. The sum of the squares of two
consecutive even natural numbers is 100. Find the numbers.
Sol. Let the two consecutive even natural
numbers be x and x +2.
As per the given condition.
x2 + (x + 2)2 =
100
∴ x2 + x2 +
4x + 4 = 100
∴ 2x2 + 4x + 4 – 100 = 0
∴ 2x2
+ 4x – 96 = 0
Dividing by 2 we get,
x2 + 2x – 48 = 0
∴ x2
– 6x + 8x – 48 = 0
∴ x
(x – 6) + 8 (x – 6) = 0
∴ (x
– 6) (x + 8) = 0
∴ x
– 6 = 0 or x + 8 = 0
∴ x
= 6 or x = – 8
x is an natural number
∴ x cannot
be – 8
∴ x
= 6
And x + 2 = 6 + 2 = 8
∴ The two consecutive even natural numbers are 6
and 8 respectively.
