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

Find the exact value of the following question:

$$ (13+2\sqrt{5})^2=?\sqrt{5}+189 $$

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?

Direction: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer.
(A) x>y
(B) x≥y
(C) x˂y
(D) x≤y
(E) x=y or the relations ship cannot be established

 I. x²- 1 = 0
II. y²+ 4y + 3 = 0. 

Find the exact value of the following question:

$$ 3{1\over2} × 3 {1\over 7}+ 5{3\over4}÷{46\over3}=?$$

Find the exact value of the following question:

$$ \sqrt {123×8+2389-1164}=? $$

Which of the following is linear equation.

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}$$.