If $x=2+2^{\frac{2}{3}}+2^{\frac{1}{3}}$,then $x^3-6x^2+6x=$

Suppose $a, b$ denote the distinct real roots of the quadratic polynomial $x^2+20x-2020$ and suppose $c, d$ denote the distinct complex roots of the quadratic polynomial $x^2-20x+2020$. Then the value of $ac(a-c)+ad(a-d)+bc(b-c)+bd(b-d)$ is

What is the minimum value of $\frac{1 - x + x^2}{1 + x + x^2}$?

Let $\tan A$ and $\tan B$, where $A, B \in (-\frac{\pi}{2}, \frac{\pi}{2})$, be the roots of the quadratic equation $x^2 - 2x - 5 = 0$. Then $20 \sin^2(\frac{A+B}{2})$ is equal to:

$p$ and $q$ are two roots of the equation $x^2+7x+3=0$. If $\frac{3p}{1-2p}$ and $\frac{3q}{1-2q}$ are the roots of $lx^2+mx+n=0$ and the greatest common divisor of $l, m, n$ is $1$,then $l-m+n=$

On each face of a cuboid,the sum of its perimeter and its area is written. Among the six numbers so written,there are three distinct numbers and they are $16, 24$ and $31$. The volume of the cuboid lies between