1) The sum of the squares of two consecutiveeven natural numbers is 10

1.	1) The sum of the squares of two consecutiveeven natural numbers is 100. Find thenumbers
Answer» 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

1) The sum of the squares of two consecutiveeven natural numbers is 100. Find thenumbers

Answer»

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