The solutions of the quadratic equation ${(3|x| - 3)^2} = |x| + 7$ which belongs to the domain of definition of the function $y = \sqrt {x(x - 3)} $ are given by
$ \pm 1/9,\; \pm 2$
$ - 1/9,\;2$
$1/9,\; - 2$
$ - 1/9,\; - 2$
The sum of all the roots of the equation $\left|x^2-8 x+15\right|-2 x+7=0$ is:
The real roots of the equation ${x^2} + 5|x| + \,\,4 = 0$ are
The complete solution of the inequation ${x^2} - 4x < 12\,{\rm{ is}}$
If $a$ and $b$ are the roots of equation $x^2-7 x-1=0$, then the value of $\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}$ is equal to $........$.
For a real number $x$, let $[x]$ denote the largest integer less than or equal to $x$, and let $\{x\}=x-[x]$. The number of solutions $x$ to the equation $[x]\{x\}=5$ with $0 \leq x \leq 2015$ is