Answer:
x=3 y=3
Step-by-step explanation:
The sum of the squares of two numbers is 18, and the product of those two numbers is 9, you just need to create an equation:
So the sum of the squares is 18, the first number will be represented as X and the second as Y:
![x^{2}+ y^{2} =18](https://tex.z-dn.net/?f=x%5E%7B2%7D%2B%20y%5E%7B2%7D%20%3D18)
And the other one is that the product of the two numbers is 9:
![xy=9](https://tex.z-dn.net/?f=xy%3D9)
We have a system of equations here, we clear X from the first one:
![x=\frac{9}{y}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B9%7D%7By%7D)
And instert that value of x in the first one:
![x^{2}+ y^{2} =18\\(\frac{9}{y} )^{2}+ y^{2} =18\\81=y^2(18-y^2)\\y^4-18y^2+81=0\\(y^2-9)(y^2-9)=0\\Y^2-9=0\\y^2=9\\y=3](https://tex.z-dn.net/?f=x%5E%7B2%7D%2B%20y%5E%7B2%7D%20%3D18%5C%5C%28%5Cfrac%7B9%7D%7By%7D%20%29%5E%7B2%7D%2B%20y%5E%7B2%7D%20%3D18%5C%5C81%3Dy%5E2%2818-y%5E2%29%5C%5Cy%5E4-18y%5E2%2B81%3D0%5C%5C%28y%5E2-9%29%28y%5E2-9%29%3D0%5C%5CY%5E2-9%3D0%5C%5Cy%5E2%3D9%5C%5Cy%3D3)
By solving this equation we get that the first number is 3.
The second number is solved by inserting the value of Y into one of the equations, in this case we will use the second:
![xy=9\\x=\frac{9}{y} \\x=\frac{9}{3} \\x=3](https://tex.z-dn.net/?f=xy%3D9%5C%5Cx%3D%5Cfrac%7B9%7D%7By%7D%20%5C%5Cx%3D%5Cfrac%7B9%7D%7B3%7D%20%5C%5Cx%3D3)
So we get that x and y are both 3.