Question

what does this mean?
find two consecutive positive even numbers the sum of whose squares is 100.

Answer 1

so it's looking for two numbers (that are positive) and even, so
2, 4, 6, 8, 10. etc.
and the squares of those numbers will add up to 100
so the square would be the numbers multiplied by themselves.
they have to be smaller than 10, since 10 * 10 itself = 100

Answer 2

so then we can go up, so they'll be in ORDER and their even, so there's the options of;
2 and 4, 4 and 6, 6 and 8
the squares of 2 and 4 only add up to 20
so that's toolittle
let's try 4 and 6
16 + 36 = 52, so too little
6 and 8
36 + 64 = 100
so that's the answer :)
6 and 8

Answer 3

good trial and error approach :)

another approach is to define 2 even consecutive numbers as:

2n and 2n+2

(2n)^2 + (2n+2)^2 = 100

4n^2 + 4n^2 +4 + 8n = 100

8n^2 + 8n + 4 = 100

8n^2 + 8n - 96 = 0

n^2 + n - 12 = 0

n = -4 or 3, -4 is out so let n=3 and we get the results already posted :)