Answer: 9 and 16
Step-by-step explanation:
Say one of the numbers is x and the other is y.
Set up a system of equations:
[tex]x + y = 25\\x^{2} + y^{2} = 337[/tex]
Move around the first equation so that you can plug it in to the second equation.
[tex]x = 25 - y[/tex]
Plug it into the second equation.
[tex](25-y)^2 + y^2 = 337[/tex]
Solve it out.
[tex](625-50y+y^2) + y^2 = 337[/tex]
[tex]625-50y+2y^2=337[/tex]
[tex]288-50y+2y^2=0[/tex]
Use the quadratic formula to solve for y.
[tex]y=\frac{-(-50)+\sqrt{(-50)^2-4(2)(288)} }{2(2)} \\\\y= 16\\y=\frac{-(-50)-\sqrt{(-50)^2-4(2)(288)} }{2(2)} \\\\y = 9[/tex]
Now plug it in and test out the values of each.
Let's do the first one first.
[tex]x + 16 = 25\\x = 9[/tex]
Wow! We can see that it is equal to the 2nd y value we produced.
But let's double check.
[tex]9^2 + 16^2 = 337[/tex]
We are correct. The order of x and y doesn't matter because we can see that the two numbers are 9 and 16. Hope that helps.
