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

The number of ordered pairs $(a, b)$ of integers such that $1 \leq a, b \leq 2021$ and the equations $x^2 - ax + b = 0$ and $x^3 - ax^2 + bx + a - b = 0$ have a common real root is

Let $p, q$ and $r$ be real numbers $(p \ne q, r \ne 0)$ such that the roots of the equation $\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}$ are equal in magnitude but opposite in sign. Then the sum of squares of these roots is equal to:

If $p$ and $q$ are distinct prime numbers and the equation $x^2 - px + q = 0$ has positive integers as its roots,then the roots of the equation are:

If the bi-quadratic equation $f(x)=x^4+2x^3-16x^2-22x+7=0$ has $2+\sqrt{3}$ as one of its roots,then which of the following is not a root of $f(x)$?

The value of $4+\frac{1}{5+\frac{1}{4+\frac{1}{5+\frac{1}{4+\ldots \ldots \infty}}}}$ is