If $p$ and $q$ are positive real numbers such that $p^2 + q^2 = 1$,what is the maximum value of $(p + q)$?

Let $\alpha, \beta (\alpha > \beta)$ be the roots of the quadratic equation $x^{2} - x - 4 = 0$. If $P_{n} = \alpha^{n} - \beta^{n}, n \in N$,then $\frac{P_{15} P_{16} - P_{14} P_{16} - P_{15}^{2} + P_{14} P_{15}}{P_{13} P_{14}}$ is equal to $......$

If $x = \sqrt[3]{{\sqrt{2} + 1}} - \sqrt[3]{{\sqrt{2} - 1}}$,then ${x^3} + 3x = $

The sum of the squares of all the roots of the equation $x^2+|2x-3|-4=0$ is:

If $a^2+b^2+c^2=1$,where $a, b, c \in \mathbb{R}$,then the set of extreme values of $ab+bc+ca$ is

Suppose $p, q, r$ are real numbers such that $q=p(4-p)$,$r=q(4-q)$,and $p=r(4-r)$. The maximum possible value of $p+q+r$ is