SSC ALGEBRA QUIZ 19

If $x=2+\sqrt{3}, y=2-\sqrt{3}, z=1$, then what is the value of $\left(\frac{x}{y z}\right)+\left(\frac{y}{x z}\right)+\left(\frac{z}{x y}\right)+2\left[\left(\frac{1}{x}\right)+\left(\frac{1}{y}\right)+\left(\frac{1}{z}\right)\right]$

If $5 x+9 y=5$ and $125 x^{3}+729 y^{3}=120$ then the value of the product of $x$ and $y$ is

What is the value of $\left(x^{2}+y^{2}+z^{2}-x y-y z-\right.$ $z x)$, when $x=197, y=197$ and $z=199$.

If $x=16$ then, $x^{4}-17 x^{3}+17 x^{2}-17 x+17=$ ?

If $x+\frac{1}{x}=\frac{5}{2}$, then what is $x^{4}-\frac{1}{x^{4}}$ equal to?

If $2 \sqrt{y}=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$

What is the value of $a^{3}+b^{3}+c^{3}-3 a b c$, when $a=95, b=96$ and $c=97$.

If $x+\frac{1}{x}=5$, the value of $x^{5}+\frac{1}{x^{5}}$ is

If $x=\frac{2 \sqrt{6}}{\sqrt{3}+\sqrt{2}}$, then the value of $\frac{x+\sqrt{2}}{x-\sqrt{2}}+\frac{x+\sqrt{3}}{x-\sqrt{3}}$ is

If $1+4 r^{2}+16 r^{4}=256$ and $1+2 r+4 r^{2}=32$, then find the value of $\frac{1}{r} + \frac{1}{r^{2}}$.