Find the roots of the following equations:
(i) x-1/x = 3, x ≠ 0
(ii) 1/x+4 - 1/x-7 = 11/30, x = -4, 7
(i) x-1/x = 3
⇒ x2 - 3x -1 = 0
On comparing this equation with ax2 + bx + c = 0, we get
a = 1, b = -3 and c = -1
By using quadratic formula, we get
x = -b±√b2 - 4ac/2a
⇒ x = 3±√9+4/2
⇒ x = 3±√13/2
∴ x = 3+√13/2 or x = 3-√13/2
(ii) 1/x+4 - 1/x-7 = 11/30
⇒ x-7-x-4/(x+4)(x-7) = 11/30
⇒ -11/(x+4)(x-7) = 11/30
⇒ (x+4)(x-7) = -30
⇒ x2 - 3x - 28 = 30
⇒ x2 - 3x + 2 = 0
⇒ x2 - 2x - x + 2 = 0
⇒ x(x - 2) - 1(x - 2) = 0
⇒ (x - 2)(x - 1) = 0
⇒ x = 1 or 2
