Question

Solve the following equation by factorisation method:

`x+1/x = 10/3, x\cancel=0`

Answer 1

Given:

`x+1/x = 10/3, x\cancel=0`

Multiply both sides by x

`x^2 + 1 = 10/3 x`

`x^2 - 10/3x+1 = 0`

3x² − 10x + 3 = 0

Product

= 3 × 3

= 9

sum = −10

3x² − 9x − x + 3 = 0

3x(x − 3) − 1(x − 3) = 0

(3x − 1) (x − 3) = 0

3x − 1 = 0

⇒ x = `1/3`

x − 3 = 0

⇒ x = 3

x = 3 or x = `1/3`