$\alpha$, $\beta$ ,$\gamma$ are roots of equatiuon $x^3 -x -1 = 0$ then equation whose roots are $\frac{1}{{\beta + \gamma }},\frac{1}{{\gamma + \alpha }},\frac{1}{{\alpha + \beta }}$ is
$x^3 -x^2 + 1 = 0$
$x^3 + x^2 -1 = 0$
$x^3 + x -1 = 0$
$x^3 -x + 1 = 0$
If $\alpha , \beta $ are the roots of the equation $x^2 - 2x + 4 = 0$ , then the value of $\alpha ^n +\beta ^n$ is
If $\alpha ,\beta ,\gamma$ are the roots of $x^3 - x - 2 = 0$, then the value of $\alpha^5 + \beta^5 + \gamma^5$ is-
If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$, then the other roots are
The number of real roots of the equation $5 + |2^x - 1| = 2^x(2^x - 2)$ is
The number of real roots of the equation $x | x |-5| x +2|+6=0$, is