How do you prove that x^2+y^2-2xy+x-y+1 is greater than 0?
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You can't. All that you can say for sure is that is nonnegative. The entire quantity will only be positive if , which you are not guaranteed.
Originally Posted by Prove It You can't. All that you can say for sure is that is nonnegative. The entire quantity will only be positive if , which you are not guaranteed. It does not matter if is negative; may be big enough to make the whole expression positive. Indeed, is clearly always positive.
Excellent proof ...My congratulations to Nehushtan Minoas
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