Question

`x^2+2sqrt2x-6=0` 

 

Answer 1

We Write 

`2sqrt2x=3sqrt2x-sqrt2x   as    x^2xx(-6)=-6x^2=3sqrt2x xx (-sqrt2x)` 

∴`x^2+2sqrt2x-6=0` 

⇒`x^2+2sqrt2x-sqrt2x-6=0` 

⇒`x(x+3sqrt2)-sqrt2 (x+3sqrt2)=0` 

⇒`(x+3sqrt2)(x-sqrt2)=0` 

⇒`x+3sqrt2=0  or  x-sqrt2=0` 

⇒`x=-3sqrt2  or  x=sqrt2` 

Hence, the roots of the given equation are `-3sqrt2` and `sqrt2`