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

If $$ {x^4}+{1\over{x^4}}$$ then find $$ {x^3}-{1\over{x^3}}=?$$

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

If $$ ({x+y\over z})=2$$ , then what is the value of $$ [{ {y\over {y-z}}}] +[{ {x\over {x-z}}}]$$.

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

If 5^√x + 12^√x = 13^√x, then x is equal to: 

simplify the following equation
$$ (1-{1\over3})(1-{1\over4})(1-{1\over5})......(1-{1\over n})$$

If $$ {a^{x}={(x+y+z)^{y}}}, a^{y}=(x+y+z)^{z}  and \ a^{z}=(x+y+z)^{x}$$ then the value of (x +y +z) is