Question

Solve the following quadratic equations by factorization:

`3x^2 - 2sqrt6x + 2 = 0`

Answer 1

We have been given

`3x^2-2sqrt6x+2=0`

`3x^2-sqrt6x-sqrt6x+2=0`

`sqrt3x(sqrt3x-sqrt2)-sqrt2(sqrt3x-sqrt2)=0`

`(sqrt3x-sqrt2)(sqrt3x-sqrt2)=0`

Therefore,

`sqrt3x-sqrt2 = 0`

`sqrt3x=sqrt2`

`x=sqrt(2/3)`

or,

`sqrt3x-sqrt2 = 0`

`sqrt3x=sqrt2`

`x=sqrt(2/3)`

Hence, `x=sqrt(2/3)` or `x=sqrt(2/3)`.