Question

The sum of two numbers is 25 and the sum of their squares is 337. Find the numbers

Answer 1

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:

$x + y = 25\\x^{2} + y^{2} = 337$

Move around the first equation so that you can plug it in to the second equation.

$x = 25 - y$

Plug it into the second equation.

$(25-y)^2 + y^2 = 337$

Solve it out.

$(625-50y+y^2) + y^2 = 337$

$625-50y+2y^2=337$

$288-50y+2y^2=0$

Use the quadratic formula to solve for y.

$y=\frac{-(-50)+\sqrt{(-50)^2-4(2)(288)} }{2(2)} \\\\y= 16\\y=\frac{-(-50)-\sqrt{(-50)^2-4(2)(288)} }{2(2)} \\\\y = 9$

Now plug it in and test out the values of each.

Let's do the first one first.

$x + 16 = 25\\x = 9$

Wow! We can see that it is equal to the 2nd y value we produced.

But let's double check.

$9^2 + 16^2 = 337$

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.