If $x = \frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} - \sqrt{2}}$ and $y = \frac{\sqrt{5} - \sqrt{2}}{\sqrt{5} + \sqrt{2}}$,then $3x^2 + 4xy - 3y^2 = $

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

For $x \in \mathbb{R}$,the minimum value of $\frac{x^2+2x+5}{x^2+4x+10}$ is

For $0 < c < b < a$,let $(a+b-2c)x^2 + (b+c-2a)x + (c+a-2b) = 0$ and $\alpha \neq 1$ be one of its roots. Then,among the two statements:
$(I)$ If $\alpha \in (-1, 0)$,then $b$ cannot be the geometric mean of $a$ and $c$.
$(II)$ If $\alpha \in (0, 1)$,then $b$ may be the geometric mean of $a$ and $c$.

For all real values of $x$,the minimum value of $\frac{1-x+x^2}{1+x+x^2}$ is

If $x+\frac{1}{x}=a$ and $x^2+\frac{1}{x^3}=b$,then $x^3+\frac{1}{x^2}$ is