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

Let $x, y, z$ be non-zero real numbers such that $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=7$ and $\frac{y}{x}+\frac{z}{y}+\frac{x}{z}=9$, then $\frac{x^3}{y^3}+\frac{y^3}{z^3}+\frac{z^3}{x^3}-3$ is equal to

A real root of the equation ${\log _4}\{ {\log _2}(\sqrt {x + 8} - \sqrt x )\} = 0$ is

If ${x^2} + 2ax + 10 - 3a > 0$ for all $x \in R$, then

Suppose $a$ is a positive real number such that $a^5-a^3+a=2$. Then,

The number of distinct real roots of the equation $x ^{7}-7 x -2=0$ is