Question

Solve the following quadratic equation:

`x/(x + 1) + (x + 1)/x = 2 4/15, x ≠ 0, 1`

Answer 1

`x/(x + 1) + (x + 1)/x = 2 4/15, x ≠ 0, -1` 

⇒ `(x^2 + (x + 1)^2)/(x(x + 1)) = 34/15` 

⇒ `(x^2 + x^2 + 2x + 1)/(x^2 + x) = 34/15` 

⇒ `(2x^2 + 2x + 1)/(x^2 + x) = 34/15` 

⇒ 30x² + 30x + 15 = 34x² + 34x 

⇒ 4x² + 4x – 15 = 0 

⇒ 4x² + 10x – 6x – 15x = 0 

⇒ 2x(2x + 5) – 3(2x + 5) = 0 

⇒ (2x + 5) (2x – 3) = 0 

⇒ 2x + 5 = 0 or 2x – 3 = 0 

⇒ `x = (-5)/2` or `2x - 3 = 0` 

Hence, `(-5)/2` and `3/2` are the roots of the given equation.