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प्रश्न
Solve the following quadratic equation:
`1/(x - 2) + 2/(x - 1) = 6/x, x ≠ 0, 1, 2`
बेरीज
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उत्तर
`1/(x - 2) + 2/(x - 1) = 6/x`
⇒ `((x - 1) + 2(x - 2))/((x - 1)(x - 2)) = 6/x`
⇒ `(3x - 5)/(x^2 - 3x + 2) = 6/x`
⇒ 3x2 – 5x = 6x2 – 18x + 12 ...[On cross multiplying]
⇒ 3x2 – 13x + 12 = 0
⇒ 3x2 – (9 + 4)x + 12 = 0
⇒ 3x2 – 9x – 4x + 12 = 0
⇒ 3x(x – 3) – 4(x – 3) = 0
⇒ (3x – 4)(x – 3) = 0
⇒ 3x – 4 = 0 or x – 3 = 0
⇒ `x = 4/3` or `x = 3`
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