Question

Solve the following quadratic equation:

`x/(x - 1) + (x - 1)/4 = 4 1/4, x ≠ 0, 1` 

Answer 1

`x/(x - 1) + (x - 1)/4 = 4 1/4, x ≠ 0, 1` 

⇒ `(x^2 + (x - 1)^2)/(x(x - 1)) = 17/4`  

⇒ `(x^2 + x^2 - 2x + 1)/(x^2 - 1) = 17/4` 

⇒ `(2x^2 - 2x + 1)/(x^2 - 1) = 17/4` 

⇒ 8x² – 8x + 4 = 17x² – 17x 

⇒ 9x² – 9x – 4 = 0 

⇒ 9x² – 12x + 3x – 4 = 0

⇒ 3x(3x – 4) + 1(3x – 4) = 0 

⇒ (3x – 4) (3x + 1) = 0

⇒ 3x – 4 = 0 or 3x + 1 = 0 

⇒ `x = 4/3` or `x = (-1)/3`  

Hence, `4/3` and `(-1)/3` are the roots of the given equation.