If $$ {x+{1\over {x}}=1}$$, then find the value of $$ {x^{208}+{x^{205}+x^{204}+x^{201}}}$$.

If $$ \sqrt {x^2+y^2}=25$$, and y=2x, find x. 

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

If bc+ab+ca=abc, then the value of $$ {b+c\over {bc(a-1)}}+{a-c\over {ac(b-1)}}+{a+b\over {ab(c-1)}}$$ is

If a+b = 1 and a³+b³+3ab=k, then the value of k is : 

If a²=b+c, b²=c+a  and c²=a+b then the  value of $$ {1\over{1+a}}+{1\over{1+b}}+{1\over{1+c}}$$ is

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

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