Find the roots of the equation .

Question

Philoid · Accepted Answer

The equation is equivalent to:

(x - 5) + (2x - 3) = (2x - 3)(x - 5)

⇒ 3x – 8 = 2x² – 13x + 15

⇒ 2x² – 16x + 23 = 0

Here, on comparing with general equation ax ² + bx + c = 0, we get

a = 2

b = - 16

c = 23

Now, Discriminant = D = (b² – 4ac)

∴ D = [256 - (4 × 2 × 23)]

= [256 - 184]

= 72

Therefore roots of the equation are given by:

x = (-b ± √D)/2a

∴ x = (16 ± √72))/4

= [16 + 6√2)/4] or [16 – 6√2/4]

= (8 + 3√2)/2 or (8 – 3√2)/2.

Thus the roots of the equation are: (8 + 3√2)/2 and (8 – 3√2)/2.