Given A B -A2-B2-2AB- what is A-B- if A B -9-

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Inequality

Given A B...

Question

Given $\begin{matrix} A B \end{matrix} = A^{2} + B^{2} + 2 A B$ , what is $A + B$ , if $\begin{matrix} A B \end{matrix} = 9$ ?

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Solution

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A = [\begin{matrix} 2 & - 1 0 & 1 \end{matrix}]

B = [\begin{matrix} 1 & 0 - 1 & - 1 \end{matrix}],

(A + B)^{2} = A^{2} + A B + B A + B^{2} = A^{2} + 2 A B + B^{2}

The lowest form of $\frac{(a + b)}{a b} - \frac{2}{(a + b)}$ if ab=1.

A_{2} + B_{2} ⟶ 2 A B

A_{2} ⇌ A + A

A + B_{2} ⟶ A B + B

A + B ⟶ A B

A_{2} + B_{2} \to 2 A B

A_{2} ⇌ A + A

A + B_{2} \to A B + B

\to

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