Question

The sum of the squares of two consecutive positive even integers is one hundred. Find the two integers.

Answer 1

x^2+(x+2)^ 2= 100
x^2+x^2+4x+4=100
2x^2+4x-96=0
x^2+2x-48=0
(x+8)(x-6)=0
x=-8 0 or 6
The problem specifies positive so the required integers are 6 and 8

Answer 2

try some numbers and see if it works

Answer 3

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Answer 4

for example 4 and 6 don't work because
\[4^2+6^2=16+36\] so try 6 and 8

Answer 5

We usually use these numbers in right triangle for hypotenuse.
3^2+4^2=5^2
6^2+8^2=10^2
5^2+12^2=13^2