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Need Explanations For The Red Part (2 variable inequality)

WannaBe

New member
Oct 4, 2013
11
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
Jan 27, 2012
196
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 \(\displaystyle (x-1)^2+(y-1)^2\ge 0\)