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प्रश्न
Solve the following quadratic equation by factorisation.
3x2 - 2√6x + 2 = 0
उत्तर
3x2 - 2√6x + 2 = 0
Using splitting the middle term method,
⇒ 3x2 - √6x - √6x + 2 = 0.
⇒ `3x^2 - sqrt(2 xx 3) x - sqrt(2 xx 3) x + 2 = 0`
⇒ 3x2 - (√2)(√3)x - (√2)(√3)x + 2 = 0.
⇒ √3x(√3x - √2) - √2(√3x - √2) = 0.
⇒ (√3x - √2)(√3x - √2) = 0
⇒ √3x - √2 = 0 or ⇒ √3x - √2 = 0
⇒ √3x = √2 or ⇒ √3x = √2
⇒ x = `sqrt2/sqrt3 = sqrt(2/3)` or ⇒ x = `sqrt2/sqrt3 = sqrt(2/3)`
Hence x = `sqrt(2/3) and sqrt(2/3)` are root of the equation.
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