$\alpha$, $\beta$ ,$\gamma$ 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 $\alpha ,\beta,\gamma$ are the roots of equation $x^3 + 2x -5 = 0$ and if equation $x^3 + bx^2 + cx + d = 0$ has roots $2 \alpha + 1, 2 \beta + 1, 2 \gamma + 1$ , then value of $|b + c + d|$ is (where $b,c,d$ are coprime)-
The set of values of $x$ which satisfy $5x + 2 < 3x + 8$ and $\frac{{x + 2}}{{x - 1}} < 4,$ is
The sum of all the real values of $x$ satisfying the equation ${2^{\left( {x - 1} \right)\left( {{x^2} + 5x - 50} \right)}} = 1$ is
The smallest value of ${x^2} - 3x + 3$ in the interval $( - 3,\,3/2)$ is
If two roots of the equation ${x^3} - 3x + 2 = 0$ are same, then the roots will be