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Question
`3x^2-2sqrt6x+2=0`
Solution
We write, `-2sqrt6x=-sqrt6x ad 3x^2xx2=6x^2=(-sqrt6x)xx(-6)`
∴ `3x^2-2sqrt6x+2=0`
⇒` 3x^2-sqrt6x-sqrt6x+2=0`
⇒ `sqrt3x(sqrt3x-sqrt2)-sqrt2(sqrt3x-sqrt2)=0`
⇒ `(sqrt3x-sqrt2)(sqrt3x-sqrt2)=0`
⇒`(sqrt3x-sqrt2)^2=0`
⇒`sqrt3x-sqrt2=0`
⇒` x=sqrt2/sqrt3=sqrt6/3`
Hence, `sqrt6/3` is the repeated root of the given equation.
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