Let $[t]$ denote the greatest integer $\leq t .$ Then the equation in $x ,[ x ]^{2}+2[ x +2]-7=0$ has

The number of real roots of the equation ${e^{\sin x}} - {e^{ - \sin x}} - 4$ $ = 0$ are

For the equation $|{x^2}| + |x| - 6 = 0$, the roots are

The number of real roots of the equation $5 + |2^x - 1| = 2^x(2^x - 2)$ is

Let $\alpha$ and $\beta$ be the roots of $x^2-6 x-2=0$, with $\alpha>\beta$. If $a_n=\alpha^n-\beta^n$ for $n \geq 1$, then the value of $\frac{a_{10}-2 a_8}{2 a_9}$ is

If the expression $\left( {mx - 1 + \frac{1}{x}} \right)$ is always non-negative, then the minimum value of m must be