The product of two numbers is 32.?

Question

Find a function that represents the sum of their squares.

please show ALL work.

Thank you very much!

Answer 1

x y = 32
y = 32 / x
x ² + y ² = x ² + (32/x) ²
P(x) = x ² + 1024 / x ²

Answer 2

xy = 32
Therefore x = 32/y and y = 32/x
So x² = 1024/ y²
and y² = 1024/x²
We need common denominators to add these
1024 / y² = 1024x² / x²y²
1024 / x² = 1024y² / x²y²
This means that x² + y² = 1024(x² + y²) / x²y²
It would be much easier if you knew one of the numbers, but there are even many integer solutions to the original problem, such as 32 and 1, 16 and 2, and 8 and 4.

Answer 3

Suppose the numbers are x and y. We have xy = 32, or y = 32/x. The sum of their squares is S = x^2 + y^2 , and using y = 32/x, we find S = x^2 + (32/x)^2.