The sum of all the solutions of the equation $(8)^{2 x}-16 \cdot(8)^x+48=0$ is :

What is the sum of all natural numbers $n$ such that the product of the digits of $n$ (in base $10$ ) is equal to $n^2-10 n-36 ?$

Let $\alpha$ and $\beta$ be the two disinct roots of the equation $x^3 + 3x^2 -1 = 0.$ The equation which has $(\alpha \beta )$ as its root is equal to

Number of solutions of equation $|x^2 -2|x||$ = $2^x$ , is

If $a,b,c$ are real and ${x^3} - 3{b^2}x + 2{c^3}$ is divisible by $x - a$ and$x - b$, then

If $\alpha $, $\beta$, $\gamma$  are roots of ${x^3} - 2{x^2} + 3x - 2 = 0$ , then the value of$\left( {\frac{{\alpha \beta }}{{\alpha  + \beta }} + \frac{{\alpha \gamma }}{{\alpha  + \gamma }} + \frac{{\beta \gamma }}{{\beta  + \gamma }}} \right)$ is