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Question
Solve the following equation by using formula :
`(1)/x + (1)/(x - 2) = 3, x ≠ 0, 2`
Solution
`(1)/x + (1)/(x - 2)`
`(x - 2 + x)/(x(x - 2))` = 3
⇒ `(2x - 2)/(x^2 - 2x)` = 3
⇒ 3x2 - 6x = 2x - 2
⇒ 3x2 - 6x - 2x + 2 = 0
⇒ 3x2 - 8x + 2 = 0
Here a = 3, b = -8, c = 2
b2 - 4ac
= (-8)2 - 4 x 3 x 2
= 64 - 24
= 40
x = `(-b ± sqrt(b^2 - 4ac))/(2a)`
= `(-(-8) ± sqrt(40))/(2 xx 3)`
= `(8 ± 2sqrt(10))/(6)`
= `(4 ± sqrt(10))/(3)`
∴ x = `(4 + sqrt(10))/(3) and (4 - sqrt(10))/(3)`.
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