Question

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

Answer 1

Answer:

Step-by-step explanation:

Let x and (x+2) be the two consecutive even natural number.

therefore

According to 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.

Answer 2

Answer:

The two consecutive even natural numbers are 6 and 8

Step-by-step explanation:

Let the two consecutive even natural numbers be x and x+2

∴ $x^{2} +(x+2)^2=100\\x^2+x^2+4x+4=100\\x^2+x^2+4x+4-100=0\\ 2x^2+4x-96=0$

When we divide it by 2 we get,

$x^2+2x-48=0\\x^2-6x+8x-48=0\\x(x-6)+8(x-6)=0\\(x+8)(x-6)=0$

∴x-6=0 or x+8=0

∴x=6 or x=-8

x is a natural number so it cannot be -8

∴x=6

∴x+2=6+2=8

∴The two consecutive even natural numbers are 6 and 8