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

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

If $a, b, c$ are three positive numbers such that the maximum value of $abc^2$ is $1/64$,then:

For what condition will the expression $a^2x^2 + bx + 1$ be positive for all $x \in R$?

If $x$ is real,the expression $\frac{x + 2}{2x^2 + 3x + 6}$ takes all values in the interval

Let $\alpha, \beta$ be the roots of the equation $x^{2}-4 \lambda x+5=0$ and $\alpha, \gamma$ be the roots of the equation $x^{2}-(3 \sqrt{2}+2 \sqrt{3}) x+7+3 \lambda \sqrt{3}=0$. If $\beta+\gamma=3 \sqrt{2}$,then $(\alpha+2 \beta+\gamma)^{2}$ is equal to