Find the value of n when $$ {n=\sqrt{n+ 2 \sqrt{n+2\sqrt{n+2\sqrt{3n}}}}}$$

If $$ {x^{2}+3{x}+1=0}$$, then the value of $$ {x^{3}+{1\over {x^{3}}}}$$

If $$ {x=a^{2\over3}-a^{-2\over3}}$$ then the value of $$ {x^{3}+3x}$$.

If $$ {x^{12}+x^{3}\over {x^{6}}}=0$$ find $$ {x^{36}+{1\over x^{36}}}$$

If $$ x={\sqrt3\over{2}}$$ then the value of $$ \sqrt{1+x}-\sqrt{1-x}$$ will be

If x + y + z=1, xy+yz+zx=-26 and x³ + y³+z³=151, then what will be the value of xyz?

If $$ x=\sqrt{\sqrt{5}+1\over {\sqrt{5}-1}}$$ then the value  of $$ {5x^2-5x-1}$$ will be:

If x + y = 1 and xy (xy – 2) = 12,then the value of x⁴ + y⁴ is: