Question

Find the roots of the equation by factorization:

`10x -1/x = 3`

Answer 1

`10x -1/x = 3`

Multiply both sides by x (where x ≠ 0):

10x² − 1 = 3x

10x² − 3x − 1 = 0

Find two numbers whose product is 10 × (−1) = −10 and sum is −3.

10x² − 5x + 2x − 1 = 0

(5x + 1) (2x − 1) = 0

5x + 1 = 0

⇒ x = `-1/5`

2x − 1 = 0

⇒ x = `1/2`

`x = 1/2, -1/5`