It is proved by counter proof that for any real number x, y, x ^ 2 + 2Y and Y ^ 2 + 2x, at least one of them is not less than - 1

It is proved by counter proof that for any real number x, y, x ^ 2 + 2Y and Y ^ 2 + 2x, at least one of them is not less than - 1

Proof: suppose that X & # 178; + 2Y and Y & # 178; + 2x are less than - 1
That is: X & # 178; + 2Y < - 1
Y²+2X＜-1
Add the two formulas to get X & # 178; + 2Y + Y & # 178; + 2x < - 2
X²+2Y+Y²+2X+1+1＜0
(X+1)²+(Y+1)²＜0
And (x + 1) &# 178;, (y + 1) &# 178; are all non negative numbers, and their sum should not be less than 0, which contradicts the above formula
So if the hypothesis does not hold, the original proposition will be proved!