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

If $|x - 2| + |x - 3| = 7$, then $x =$

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

Let $a, b, c$ be non-zero real roots of the equation $x^3+a x^2+b x+c=0$. Then,

Let $p$ and $q$ be two real numbers such that $p+q=$ 3 and $p^{4}+q^{4}=369$. Then $\left(\frac{1}{p}+\frac{1}{q}\right)^{-2}$ is equal to

The number of solutions, of the equation $\mathrm{e}^{\sin x}-2 e^{-\sin x}=2$ is