If the roots of the equation $5x^2 - 7x + k = 0$ are reciprocal to each other,then the value of $k$ is:

If $\alpha, \beta, \gamma$ are roots of $x^3 - 2x^2 + 3x - 2 = 0$,then the value of $\left( \frac{\alpha \beta}{\alpha + \beta} + \frac{\alpha \gamma}{\alpha + \gamma} + \frac{\beta \gamma}{\beta + \gamma} \right)$ is

If $\alpha, \beta$ are roots of the equation $x^{2}+5 \sqrt{2} x+10=0$,$\alpha > \beta$ and $P_{n}=\alpha^{n}-\beta^{n}$ for each positive integer $n$,then the value of $\left(\frac{P_{17} P_{20}+5 \sqrt{2} P_{17} P_{19}}{P_{18} P_{19}+5 \sqrt{2} P_{18}^{2}}\right)$ is equal to $....$

If $a+b+c=1$,$ab+bc+ca=2$ and $abc=3$,then the value of $a^{4}+b^{4}+c^{4}$ is equal to $...$

If $\alpha$ and $\beta$ are the roots of the equation $7x^{2}-3x-2=0$,then the value of $\frac{\alpha}{1-\alpha^{2}}+\frac{\beta}{1-\beta^{2}}$ is equal to

If the sum of the squares of the reciprocals of the roots $\alpha$ and $\beta$ of the equation $3x^{2} + \lambda x - 1 = 0$ is $15$,then $6(\alpha^{3} + \beta^{3})^{2}$ is equal to