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

If the sum of all the roots of the equation $e^{2 x}-11 e^{x}-45 e^{-x}+\frac{81}{2}=0$ is $\log _{ e } P$, then $p$ is equal to

Suppose $a$ is a positive real number such that $a^5-a^3+a=2$. Then,

Let $\alpha$ and $\beta$ be the roots of the equation $5 x^{2}+6 x-2=0 .$ If $S_{n}=\alpha^{n}+\beta^{n}, n=1,2,3 \ldots$ then :

Let $\lambda \in R$ and let the equation $E$ be $| x |^2-2| x |+|\lambda-3|=0$. Then the largest element in the set $S =$ $\{ x +\lambda: x$ is an integer solution of $E \}$ is $..........$

The sum of all non-integer roots of the equation $x^5-6 x^4+11 x^3-5 x^2-3 x+2=0$ is