What is the minimum value of the algebraic formula 1 / - 2-A ^ 2-2ab-b ^ 2? When the algebraic formula takes the minimum value, what conditions should a and B satisfy? | Math enthusiast | Mathematical art

What is the minimum value of the algebraic formula 1 / - 2-A ^ 2-2ab-b ^ 2? When the algebraic formula takes the minimum value, what conditions should a and B satisfy?

Let's look at this formula first, and the last three terms can form a complete square formula
1. Deformation 1 / - 2-A ^ 2-2ab-b ^ 2
=1/-2-（a^2+2ab+b^2）
=1/-2-（a+b）^2
2 to make the formula the simplest, then (a + b) ^ 2 = o
Therefore, AB satisfies the condition that a and B are opposite to each other

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