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

If $$ {(x-5)^{2} +{(y-2)^{2}}+{(z-9)^{2}=0}}$$ then what is the value of (x+y-z)?

If $$ {t^{2}-4t+1=0}$$ then what is the value of $${t^{3}+{1\over {t^{3}}}}$$ ?

If $$ {x+{1\over 16x}}=1 $$, then $$ {64x^{3}+{1\over 64x^{3}}}$$ will be:

If $$ {(x+{1 \over{x}})^{2}}=3$$, the value of of $$  {x^{206}+x^{200}+x^{90}+x^{84}+x^{18}+x^{12}+x^{6}+1}$$

If $$ {x=2-2^{1\over 3}+2 ^{2\over 3}}$$, then the value of $$ {x^{3}-6x^{2}+18x+18}$$.

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

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