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Question
`sqrt3x^2-2sqrt2x-2sqrt3=0`
Solution
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`
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