The roots of the equation $x^{2}+px+q=0$ are equal if:

If $x+\frac{1}{y}=1$ and $y+\frac{1}{z}=1$,then find the value of $z+\frac{1}{x}$.

Two positive distinct numbers $a$ and $b$ each differ from their reciprocal by $1$. The value of $a + b$ is

Let $x_1, x_2, x_3 \in R - \{0\}$,$x_1 + x_2 + x_3 \neq 0$ and $\frac{1}{x_1} + \frac{1}{x_2} + \frac{1}{x_3} = \frac{1}{x_1 + x_2 + x_3}$. Then $\frac{1}{x_1^n + x_2^n + x_3^n} = \frac{1}{x_1^n} + \frac{1}{x_2^n} + \frac{1}{x_3^n}$ holds good for:

Solve the given two equations and select the correct answer from the given options.
$I.$ $16 x^{2}+20 x+6=0$
$II.$ $10 y^{2}+38 y+24=0$

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-7 \sqrt{7} x+84=0$
$II.$ $y^{2}-5 \sqrt{5} y+30=0$