The sum of two numbers is 20. What is the least possible sum of their squares.
2. The attempt at a solution
Before I show my work, I'm pretty sure I have the answer. I think it's 200. If you add 10 and 10, you will have 20. If you square 10 you get 100, thus the sum of the squares would be 200. If you used any other numbers to get a sum of 20 (i.e. 1 and 19, 2 and 18, 3 and 17, etc.), and you'd end up with a number over 200. For example, 18 + 2 = 20, 18^2 = 324, 2^2 = 4, 324 + 4 = 328. For all numbers other than 10 and 10, you'll get an answer over 200.
It's just I'm not exactly sure how to show my work for that. The only thing I can come up with is this:
The equation to show that the sum of two numbers equalling 20 is x + x = 20.
To show the squares of those numbers would be x^2 + x^2 = 20.
Therefore, 2x^2 = 20.
x^2 = 20/2
x^2 = 10
Am I on the right track with this?