If the expression $7+6x-3x^2$ attains its extreme value $\beta$ at $x=\alpha$,then the sum of the squares of the roots of the equation $x^2+\alpha x-\beta=0$ is

For $x \in R$, the least value of $\frac{x^2-6x+5}{x^2+2x+1}$ is

Let $\alpha, \beta$ be the roots of the equation $x^2 - |a|x - |b| = 0$ such that $|\alpha| < |\beta|$. If $|a| < \beta - 1$,then the positive root of $\log_{|\alpha|} \left( \frac{x^2}{\beta^2} \right) - 1 = 0$ is

If $x$ is real,then the maximum and minimum values of the expression $\frac{x^2 + 14x + 9}{x^2 + 2x + 3}$ are

The number of different possible values for the sum $x+y+z$,where $x, y, z$ are real numbers such that $x^4+4y^4+16z^4+64=32xyz$ is

Let $p$ and $q$ be two real numbers such that $p+q=3$ and $p^{4}+q^{4}=369$. Then $\left(\frac{1}{p}+\frac{1}{q}\right)^{-2}$ is equal to