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Question
Solve the following equation by using formula :
`(3x - 4)/(7) + (7)/(3x - 4) = (5)/(2), x ≠ (4)/(3)`
Solution
`(3x - 4)/(7) + (7)/(3x - 4) = (5)/(2), x ≠ (4)/(3)`
let `(3x – 4)/(7)` = y, then
`y + (1)/y = (5)/(2)`
⇒ 2y2 + 2 = 5y
⇒ 2y2 – 5y + 2 = 0
⇒ 2y2 – y – 4y + 2 = 0
⇒ y(2y – 1) –2(2y – 1) = 0
⇒ (2y – 1)(y – 2) = 0
Either 2y – 1 = 0,
then 2y = 1
⇒ y = `(1)/(2)`
or
y – 2 = 0,
then y = 2
When y = `(1)/(2)`,
then `(3x - 4)/(7) = (1)/(2)`
⇒ 6x – 8 = 7
⇒ 6x = 7 + 8
⇒ 6x = 15
⇒ x = `(15)/(6) = (5)/(2)`
y = 2, then
`(3x - 4)/(7) = (2)/(1)`
⇒ 3x – 4 = 14
⇒ 3x = 14 + 4 = 18
⇒ x = `(18)/(3)` = 6
∴ x = 6, `(5)/(2)`.
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