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प्रश्न
Solve the following quadratic equation:
`3x^2 - 2sqrt(6)x + 2 = 0`
बेरीज
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उत्तर
We write, `-2sqrt(6)x = -sqrt(6)x` as `3x^2 xx 2 = 6x^2 = (-sqrt(6)x) xx (-sqrt(6)x)`
∴ `3x^2 - 2sqrt(6)x + 2 = 0`
⇒ `3x^2 - sqrt(6)x - sqrt(6)x + 2 = 0`
⇒ `sqrt(3)x(sqrt(3)x - sqrt(2)) - sqrt(2)(sqrt(3)x - sqrt(2)) = 0`
⇒ `(sqrt(3)x - sqrt(2))(sqrt(3)x - sqrt(2)) = 0`
⇒ `(sqrt(3)x - sqrt(2))^2 = 0`
⇒ `sqrt(3)x - sqrt(2) = 0`
⇒ `x = sqrt(2)/sqrt(3) = sqrt(6)/3`
Hence, `sqrt(6)/3` is the repeated root of the given equation.
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