Question

`sqrt3x^2-2sqrt2x-2sqrt3=0` 

 

Answer 1

We write, `3sqrt2x=-3sqrt2x+sqrt2x  as  sqrt3x^2xx(-2sqrt3)=-6x^2=(-3sqrt2x)xx(sqrt-2x)` 

∴ `sqrt3x^2-2sqrt2x-2sqrt3=0` 

⇒` sqrt3x^2-3sqrt2x+sqrt2x-2sqrt3=0` 

⇒`sqrt3x(x-sqrt6)+sqrt2(x-sqrt6)=0` 

⇒`(x-sqrt6)(sqrt3x+sqrt2)=0` 

⇒`x-sqrt6=0  or  sqrt3x+sqrt2=0` 

⇒`x-sqrt6=0  or =sqrt3x+sqrt2=0`  

⇒`x-sqrt6=  or  x=-sqrt2/sqrt3=-sqrt6/3` 

Hence, the roots of the given equation are `sqrt6  and  -sqrt6/3`