Question

Solve the following quadratic equation:

`(3x - 4)/7 + 7/(3x - 4) = 5/2, x ≠ 4/3`

Answer 1

`(3x - 4)/7 + 7/(3x - 4) = 5/2, x ≠ 4/3`

⇒`((3x - 4)^2 + 49)/(7(3x - 4)) = 5/2` 

⇒ `(9x^2 - 24x + 16 + 49)/(21x - 28) = 5/2` 

⇒ 18x² – 48x + 130 = 105x – 140 

⇒ 18x² – 153x + 270 = 0 

⇒ 2x² – 17x + 30 = 0

⇒ 2x² – 12x – 5x + 30 = 0 

⇒ 2x(x – 6) – 5(x – 6) = 0 

⇒ (x – 6)(2x – 5) = 0 

⇒ x – 6 = 0 or 2x – 5 = 0 

⇒ `x = 6` or `x = 5/2` 

Hence, 6 and `5/2` are the roots of the given equation.