The minimum value of $\frac{9 \cdot 3^{2 x}+6 \cdot 3^x+4}{9 \cdot 3^{2 x}-6 \cdot 3^x+4}$ is

$p$ is non-zero real number. If the equation whose roots are the squares of the roots of the equation $x^3-p x^2+p x-1=0$ is identical with the given equation, then $p=$

Let $S$ be the set of all possible integral values of $\lambda$ in the interval $(-3,7)$ for which the roots of the quadratic equation $\lambda x^2+13 x+7=0$ are all rational numbers. Then the sum of the elements in $S$ is

$\alpha$ is the maximum value of $1-2 x-5 x^2$ and $\beta$ is the minimum value of $x^2-2 x+r$. If $5 \alpha x^2+\beta x+6>0$ for all real values $x$, then the interval in which $r$ lies is