The sum of two numbers is 12. The sum of the squares of the same two numbers is 90. What are the two numbers?

We get a system of equations:

a+b=12

a2+b2=90.

Replace 12-a for b, and we get:

a2+(12-a)2=90

2a2-24a+144=90

2a2-24a+54=0

a2-12a+27=0

a1=9

a2=3

Because of symmetry, we get two equivalent solutions:

a=9, b=3

or

a=3,b=9