Need Explanations For The Red Part (2 variable inequality)

WannaBe

New member
Prove that for any two numbers x,y we have [(x^2 + y^2)/2] >= x + y - 1

Solution)

For any number a we have have a^2 > 0. So,

(x-1)^2 + (y-1)^2 >= 0

And if we solve this we get the solution.

I don't get the red part.

Plato

Well-known member
MHB Math Helper
Re: Need Explanations For The Red Part

Prove that for any two numbers x,y we have [(x^2 + y^2)/2] >= x + y - 1
Solution)
For any number a we have have a^2 > 0. So,
(x-1)^2 + (y-1)^2 >= 0

And if we solve this we get the solution.
If for all $$\displaystyle a$$ we have $$\displaystyle a^2\ge 0$$ then $$\displaystyle (x-1)^2\ge 0~\&~(y-1)^2\ge 0$$.

Add those to together and get $$\displaystyle (x-1)^2+(y-1)^2\ge 0$$