Question 162
Consider the polynomials $P(x)=x^{3}+a x^{2}+b x+c, Q(x)=x^{3}+A x^{2}+B x+C$ ($x$ is the variable, $a, b, c, A, B, C$ are parameters). We know that the three roots of $P$ are positive and that the roots of $Q$ are the inverse numbers of the roots of $P$. Try that $a \cdot A\gt 9, b \cdot B\gt 9$.