B1. Let $a$ and $b$ be positive real numbers whose product is 1, and the sum of their squares is 4. Calculate the value of the expression $a^{-3}+b^{-3}$. The result should be exact.
B1. Given $a^{2}+b^{2}=4$ and $a b=1$, we have $(a+b)^{2}=a^{2}+b^{2}+2 a b=4+2=6$ or $a+b=\sqrt{6}$, since both $a$ and $b$ are positive numbers. It follows that

$$
\frac{1}{a^{3}}+\frac{1}{b^{3}}=\frac{a^{3}+b^{3}}{a^{3} b^{3}}=\frac{(a+b)^{3}-3 a b(a+b)}{a^{3} b^{3}}=\frac{6 \sqrt{6}-3 \cdot 1 \cdot \sqrt{6}}{1}=3 \sqrt{6}
$$

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Inserting the given data and calculating the final result . ..................................................