Question

Sum of squares of to consecutive natural even numbers is 244 find the numbers.​

Answer 1

Let the first even natural number be x.

∴ the next consecutive even natural number will be (x + 2).

According to the given condition,

x2 + (x + 2)2 = 244

∴ x2 + x2 + 4x + 4 = 244

∴ 2x2 + 4x + 4 – 244 = 0

∴ 2x2 + 4x – 240 = 0

∴ x2 + 2x – 120 = 0 …[Dividing both sides by 2]

∴ x2 + 12x – 10x – 120 = 0

∴ x(x + 12) – 10 (x + 12) = 0

∴ (x + 12) (x – 10) = 0

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get

x + 12 = 0 or x – 10 = 0

∴ x = -12

or ,x = 10

But, natural number cannot be negative.

so, x = 10 and x + 2 = 10 + 2 = 12

∴ The two consecutive even natural numbers are 10 and 12.

HOPE THIS HELPS YOU ☺️