If $$ {x+{1\over x}}=3$$ then find the value of $$ {x^2}-{1\over {x^2}}$$:

If a-b=10 and ab=-21, then what is the value of a³-b³?

If a+b=2c, find $${a\over a-c}+{c\over b-c}?$$

If then the value of

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

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

 $${a\over b}={2\over3}$$ and $${b\over c}={4\over5}$$ then the ratio  $${a+b}\over {b+c}$$ equal to: