Which of the following is reducible to a quadratic equation?

 $$(A)\ (m+1)-\frac1{(m+1)}=65\\ \ \\ (B) \ x^3+3x=2x^3-4x^2 \\ \ \\ (C) \ (a+b)^2=\frac3b\\ \ \\ (D) \ x+(3x-2)=\frac1{x^2} -6$$

Correct option is A

Concept Used:

General form of quadratic equation:

​$$ax^2+bx+c=0$$​​

Solution: 

Solving each statement; 

(A) : (m + 1) - $$\frac{1}{m+1}$$ = 65

Let  y = m + 1  The equation becomes:
y -  $$\frac{1}{y}$$​ = 65

y²​ - 1 = 65y

y² - 65y - 1 = 0 

This is a quadratic equation.

(B):    x³ + 3x - 2x³- 4x³  = 0 
Rearrange terms:

​x³ + 3x - 2x³ + 4x³  = 0

​-x³ + 4x²+ 3x = 0

x(-x² + 4x + 3) = 0
This is not a quadratic equation.

(C): 
a² + 2ab + b²=  $$\frac{3}{b}$$ 

b(a² + 2ab + b²) = 3

This is not a quadratic equation.

(D):  x + (3x - 2) = $$\frac{1}{x^2}$$​​ - 6

x + 3x - 2  =  $$\frac{1}{x^2}$$  - 6

4x - 2 + 6  =   $$\frac{1}{x^2}$$ 

4x + 4  =   $$\frac{1}{x^2}$$ 

4x³ + 4x²=  1
This is not a quadratic equation.
Thus, only statement (A) is correct