Question

Solve the following quadratic equation:

`a/((x - b)) + b/((x - a)) = 2, x ≠ b, a`

Answer 1

`a/((x - b)) + b/((x - a)) = 2` 

⇒ `[a/((x - b)) - 1] + [b/((x - b)) - 1] = 0` 

⇒ `(a - (x - b))/(x - b) + (b - (x - b))/(x - b) = 0` 

⇒ `(a - x + b)[1/((x - b)) + 1/((x - a))] = 0` 

⇒ `(a - x + b)[((x - a) + (x - b))/((x - b)(x - a))] = 0` 

⇒ `(a - x + b) [(2x - (a + b))/((x - b)(x - a))] = 0` 

⇒ (a – x + b)[2x – (a + b)] = 0

⇒ a – x + b = 0 or 2x – (a + b) = 0 

⇒ `x = a + b` or `x = (a + b)/2` 

Hence, the roots of the equation are `(a + b)` and `((a + b)/2)`.