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प्रश्न
Solve the following quadratic equation:
`4sqrt(6)x^2 - 13x - 2sqrt(6) = 0`
बेरीज
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उत्तर
Given:
`4sqrt(6)x^2 - 13x - 2sqrt(6) = 0`
⇒ `4sqrt(6)x^2 - 16x + 3x - 2sqrt(6) = 0`
⇒ `4sqrt(2)x(sqrt(3)x - 2sqrt(2)) + sqrt(3)(sqrt(3)x - 2sqrt(2)) = 0`
⇒ `(4sqrt(2)x + sqrt(3))(sqrt(3)x - 2sqrt(2)) = 0`
⇒ `4sqrt(2)x + sqrt(3) = 0` or `sqrt(3)x - 2sqrt(2) = 0`
⇒ `x = (-sqrt(3))/(4sqrt(2))= (-sqrt(3) xx sqrt(2))/(4sqrt(2) xx sqrt(2)) = (-sqrt(8))/8` or `x = (2sqrt(2))/sqrt(3) = (2sqrt(2) xx sqrt(3))/(sqrt(3) xx sqrt(3)) = (2sqrt(6))/3`
Hence, the roots of the equation are `-sqrt(6)/8` and `(2sqrt(6))/3`.
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