If $x = \frac{1}{2} \left( \sqrt{7} + \frac{1}{\sqrt{7}} \right)$, then $\frac{\sqrt{x^2 - 1}}{x - \sqrt{x^2 - 1}}$ is equal to

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

If $a$ and $b$ are arbitrary positive real numbers, then the least possible value of $\frac{6a}{5b} + \frac{10b}{3a}$ is

Let $a, b \in \mathbb{R}$ be such that the equation $ax^{2}-2bx+15=0$ has a repeated root $\alpha$. If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-2bx+21=0$,then $\alpha^{2}+\beta^{2}$ is equal to

If $x$ is real, then the value of $\frac{x^2-3x+4}{x^2+3x+4}$ lies in the interval

After the roots of the equation $6x^3 + 7x^2 - 4x - 2 = 0$ are diminished by $h$,if the transformed equation does not contain the $x^2$ term,then the product of all the possible values of $h$ is