Question

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

Answer 1

8 and 6

= 8sq. + 6sq.
=64 + 36
= 100

Answer 2

$\purple{\boxed{\huge Answer}}$

let n be a number. Let n+2 be the other number. Then:

n²+(n+2)²=100

n²+n²+4n+4=100

2n²+4n+4=100

n²+2n+2=50

n²+2n-48=0

(n-6)(n-8)=0

(n-6)=0 or (n-8)=0

n=6 or n=8

When n=6 then n+2= 8 and we get 6²+8²=36+64=100.

When n=8 then n+2=10 and we get 8²+10²=64+100=164.

Clearly n=6 and n+2=8 is correct.

The 2 consecutive even numbers whose squares add up to 100 is 6 and 8.