If $\sqrt{2} \sin^2 x + (3\sqrt{2} + 1) \sin x + 3 > 0$ and $x^2 - 7x + 10 < 0$,then $x$ lies in the interval

If the equation whose roots are $p$ times the roots of the equation $x^4-2ax^3+4bx^2+8ax+16=0$ is a reciprocal equation,then $|p|=$ :

If $\alpha_1, \beta_1, \gamma_1, \delta_1$ are the roots of the equation $a x^4+b x^3+c x^2+d x+e=0$ and $\alpha_2, \beta_2, \gamma_2, \delta_2$ are the roots of the equation $e x^4+d x^3+c x^2+b x+a=0$ such that $0 < \alpha_1 < \beta_1 < \gamma_1 < \delta_1$,$0 < \alpha_2 < \beta_2 < \gamma_2 < \delta_2$,$\alpha_1-\delta_2=2$,$\beta_1-\gamma_2=2$,$\gamma_1-\beta_2=4$,and $\delta_1-\alpha_2=4$,then $a+b+c+d+e=$

The number of triples $(x, y, z)$ of real numbers satisfying the equation $x^4+y^4+z^4+1=4xyz$ 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 difference between the greatest and least values of $\frac{x^2-x+1}{x^2+x+1}$ is