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the sum of the squares pf two postive consecutive even integers is 41. Find the integers.

Is it?

3 and 4
4 and 5
5 and 6

its 4 and 5

Right.

the number are even
so let the first be x
then the second is x+2

x^2 + (x+2)^2 = 41
x^2 + x^2 + 4x + 4 = 41
2x^2 + 4x - 37 = 0

No integer solution

We could tell from the beginning that this problem has no solution
the square of any even integer is even
the sum of two even number is even, but 41 is odd, so NO WAY!

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