(Q2)Find the roots of the equation x-
1
3x
 =
1
6
(x ≠ 0)

Answer:

We have x-
1
3x
 =
1
6

6x2 - x - 2 = 0

6x2 - x - 2 = 6x2 + x - 4x - 2

= x (x + 1)-2(x + 1)

=(x - 2)(x + 1)

The roots of 6x2- x - 2 = 0 are the values of x for which (x - 2)(x + 1) = 0

Therefore, x - 2 = 0 or x + 1 = 0,

x =
2
 or x = -
1
Therefore, the roots of 6x2- x - 2 = 0 are
2
 and -
1
 .
We verify the roots, by checking that
2
 and -
1
 satisfy 6x2- x - 2 = 0