Question

Solve the following quadratic equation by factorisation.
3x² - 2√6x + 2 = 0

Answer 1

3x² - 2√6x + 2 = 0

Using splitting the middle term method,

⇒ 3x² - √6x - √6x + 2 = 0.

⇒ `3x^2 - sqrt(2 xx 3) x - sqrt(2 xx 3) x + 2 = 0`

⇒ 3x² - (√2)(√3)x - (√2)(√3)x + 2 = 0.

⇒ √3x(√3x - √2) - √2(√3x - √2) = 0.

⇒ (√3x - √2)(√3x - √2) = 0

⇒ √3x - √2 = 0     or    ⇒ √3x - √2 = 0

⇒ √3x = √2          or    ⇒ √3x = √2

⇒ x = `sqrt2/sqrt3 = sqrt(2/3)`  or ⇒ x = `sqrt2/sqrt3 = sqrt(2/3)` 

Hence x = `sqrt(2/3) and sqrt(2/3)` are root of the equation.