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

Express 15625 as a power of 5?

Directions: In the following question, two equations are given in variables X and Y. You have to solve these equations and determine the relation between X and Y.

I. X³ = 125
II. Y³ = 8

Directions: In the following question, two equations are given in variables X and Y. You have to solve these equations and determine the relation between X and Y.

I. 2x + 3y = 52
II. 5x – 2y = 16

Directions: In the following question, two equations are given in variables X and Y. You have to solve these equations and determine the relation between X and Y.

I. X² – 5x + 6 = 0
II. 2y² – 7y +3 = 0

Direction: In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x² – 12x + 32 = 0
II. 2y² – 9y + 10 = 0