Question

Solve the following quadratic equation:

`3((7x + 1)/(5x - 3)) - 4((5x - 3)/(7x + 1)) = 11, x ≠ 3/5, (-1)/7`

Answer 1

`3((7x + 1)/(5x - 3)) - 4((5x - 3)/(7x + 1)) = 11, x ≠ 3/5, (-1)/7` 

⇒ `(3(7x + 1)^2 - 4(5x - 3)^2)/((5x - 3)(7x + 1)) = 11`

⇒ `(3(49x^2 + 14x + 1) - 4(25x^3 - 30x + 9))/(35x^2 - 16x - 3) = 11` 

⇒ `(147x^2 + 42x + 3 - 100x^2 + 120x - 36)/(35x^2 - 16x - 3) = 11`  

⇒ `(47x^2 + 162x - 33)/(35x^2 - 16x - 3) = 11` 

⇒ 47x² + 162x – 33 = 385x² – 176x – 33 

⇒ 338x² – 338x = 0 

⇒ 338x(x – 1) = 0 

⇒ x = 0 or x – 1 = 0 

⇒ x = 0 or x = 1 

Hence, 0 and 1 are the roots of the given equation.