Solve this equation by factoring. Remember va vb = vab...

Question

Solve this equation by factoring. Remember √a √b = √ab
√6 x^2-x-√6 =0

Answer 1

√6 x² - x - √6 = 0

 

Start by observing that √6 = √2 √3

 

Since we need the linear term to have coefficient -1 = 2 - 3 = (√2)² - (√3)², we get the following factorization:

 

(√3 x + √2)(√2 x - √3) = 0

 

From here, we see that the two roots are:

 

1. x = -√2 / √3 = -√6 / 3

 

2. x = √3 / √2 = √6 / 2