$$ ({2+\sqrt{5}})$$ and $$ ({2-\sqrt{5}})$$ is a quadratic equation with roots.

Factor of $$ {12x^{2}+7y^{2}-12}$$ is__

If $$ {x^2-12x+33=0}$$, then what is the value of $${(x-4)^2+[{1\over({x-4})^2}}]$$.

If one root of the equation $$ {Ax^2+Bx+C=0}$$ is two and a half times the others, then which of the following is True?

If α and β are the roots of equation $$ {x^2-2x+4=0}$$, then what is the equation whose roots are ${α^3}\over{β^2}$$ and $${β^3}\over{α^2}$$.

If α and β are the roots of the equation x² + x - 1 = 0, then what is the equation whose roots are and α⁵ and β⁵ ? 

If  $$  \left( x^2+{1\over x^2} \right)- \left( x - {1\over 4} \right)- 7 =0 $$ then two value of x are :

α and β  is two root of a equations $$2x^2-7x+ 12=0 $$ then the value of $$ {α \over β }  + {β \over α }=? $$