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The sum of the squares of two consecutive even natural numbers is 100. Find the numbers.
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.