If the roots of the equation $8{x^3} - 14{x^2} + 7x - 1 = 0$ are in $G.P.$, then the roots are

Let the sum of the maximum and the minimum values of the function $f(x)=\frac{2 x^2-3 x+8}{2 x^2+3 x+8}$ be $\frac{m}{n}$, where $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$. Then $\mathrm{m}+\mathrm{n}$ is equal to :

If $x$ is real, then the value of $\frac{{{x^2} + 34x - 71}}{{{x^2} + 2x - 7}}$ does not lie between

$\alpha$, $\beta$ ,$\gamma$  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 \in R:|x - 2|\,\, = {x^2}\} = $

If $a,b,c$ are distinct real numbers  and $a^3 + b^3 + c^3 = 3abc$ , then the equation $ax^2 + bx + c = 0$ has two roots, out of which one root is