Question

Solve the following equation by factorisation method:

`x = (4x+1)/5x, x = 0`

Answer 1

Given:

`x = (4x+1)/5x, x = 0`

Multiply both sides by 5x:

5x² = 4x + 1

5x² − 4x − 1 = 0

a = 5, b = −4, c = −1

a × c 

= −5

Numbers whose product = −5 and sum = −4.

These numbers are −5 and 1.

5x² − 5x + x − 1 = 0

5x(x − 1) + 1(x − 1) = 0

(5x + 1) (x − 1) = 0

5x + 1 = 0

⇒ x = −`1/5`

x − 1 = 0

⇒ x = 1

x = 1 or x = −`1/5`