If average of two x and $$1\over x$$ (where x ≠ 0) is A, what will be the average of x³ and $$1\over {x^3}$$?

If $$ {P={96\over95×97}},{Q={97\over96×98}}$$ and $$ {R={1\over97}}$$ then which of the following is True?

If a =500, b=502 and c=504, then the value of a³ +b³ +c³-3abc

If (a-b)=-3 , (b-c)=5 and (c-a)=-2, then the value of $$ {a^{3}+b^{3}+c^{3}-3abc\over a+b+c}$$.

If $$ {x+{1\over x}=\sqrt{3}}$$ then $$ {x^{48}+x^{378\over7}+x^{726\over11}+x^{60}}$$ is equal to

Value of $$ \sqrt{6+\sqrt {6+\sqrt {6+....}}}$$

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

Given k = -3. Find the value of $$ {k^3+3k}$$.