Question

`4sqrt6x^2-13x-2sqrt6=0`  

Answer 1

`4sqrt6x^2-13x-2sqrt6=0` 

⇒`4sqrt6x^2-16x+3x-2sqrt6=0` 

⇒` 4sqrt2x(sqrt3x-2sqrt2)+sqrt3(sqrt3x-2sqrt2)=0`  

⇒`(4sqrt2x+sqrt3)(sqrt3x-2sqrt2)=0` 

⇒`4sqrt2x+sqrt3=0 or sqrt3x-2sqrt2=0` 

⇒`x=-sqrt3/(4sqrt2)=-(sqrt3xxsqrt2)/(4sqrt2xxsqrt2)=-sqrt8/8 or x=(2sqrt2)/sqrt3=(2sqrt2xxsqrt3)/(sqrt3xxsqrt3)=(2sqrt6)/3` 

Hence, the roots of the equation are `-sqrt6/8 and (2sqrt6)/3`