Answer:
The answers are:
\(1^2+8^2=65\\4^2+7^2=65\)
Step-by-step explanation:
In order to determine the pairs of numbers, we have to know about the equation of this case.
Given:
x=first number
y=second number
\(x^2+y^2=65\)
With this equation, we can find a lot of pairs of numbers which fulfill the equation. But, in case that we need just whole numbers, we only have to replace a whole number in any variable and determine the value of the other variable.
\(x=1\\1^2+y^2=65\\y^2=65-1\\y^2=64\\y=\sqrt{64}\\y=8\\1^2+8^2=65\)
\(x=4\\4^2+y^2=65\\y^2=65-16\\y^2=49\\y=\sqrt{49}\\y=7\\4^2+7^2=65\)
Finally, the two pairs of numbers are:
\(1^2+8^2=65\\4^2+7^2=65\)
