What are the roots of the equation log₁₀(x²-6x+45) =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 ? 

A root of equation $$({ax}^2+bx+c)$$ (where a, b and c are rational numbers) is 5 +3√3. What is the value of $$({a}^2+b^2+c^2) / (a+b+c) ? $$

Direction: In the following questions two equations numbered I and II are given. You have to solve both the equations and Give answer

Give answer (A) If x > y
Give answer (B) if x ≥ y
Give answer (C) if x<y
Give answer (D) If x ≤ y
Give answer (E) if x=y or the relationship cannot be established.

 I. x² – 7x+ 12=0
II. y²-12y+32 =0

If 4x+5y=83 and $$ \ {3x\over2y}={21\over22}$$then what is the value of y-x ?

Find the exact value of the following question:

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

Solve: 0.05 × 0.4 

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