In the real number system, the equation $\sqrt{x+3-4 \sqrt{x-1}}+\sqrt{x+8-6 \sqrt{x-1}}=1$ has

Consider the equation $(1+a+b)^2=3\left(1+a^2+b^{2})\right.$ where $a, b$ are real numbers. Then,

The sum of all integral values of $\mathrm{k}(\mathrm{k} \neq 0$ ) for which the equation $\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k}$ in $x$ has no real roots, is ..... .

The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ is

The set of all $a \in R$ for which the equation $x | x -1|+| x +2|+a=0$ has exactly one real root is:

If $a, b, c$ are real numbers such that $a+b+c=0$ and $a^2+b^2+c^2=1$, then $(3 a+5 b-8 c)^2+(-8 a+3 b+5 c)^2$ $+(5 a-8 b+3 c)^2$ is equal to