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It is proved that if a, B ∈ R, then at least one of a ^ 2 + AB and B ^ 2 + AB is non negative Good answer points
Suppose that both a ^ 2 + AB and B ^ 2 + AB are negative numbers, then
(a^2+ab)+(b^2+ab)＜0
a^2+2ab+b^2＜0
(a+b)^2＜0
We know that the square of any number is nonnegative,
So (a + b) ^ 2 is also nonnegative,
It doesn't match the hypothesis, so
At least one of a ^ 2 + AB and B ^ 2 + AB is non negative
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