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Question
Solve the following equation by using formula :
`(2x + 5)/(3x + 4) = (x + 1)/(x + 3)`
Solution
`(2x + 5)/(3x + 4) = (x + 1)/(x + 3)`
(2x + 5)(x + 3) = (x + 1)(3x + 4)
2x2 + 6x + 5x + 15 = 3x2 + 4x + 3x + 4
⇒ 3x2 + 7x + 4 – 2x2 - 11x – 15 = 0
⇒ x2 – 4x – 11 = 0
Here a = 1, b = –4, c = –11
D = b2 – 4ac
= (–4)2 – 4 x 1 x (–11)
= 16 + 44
= 60
∵ x = `(-b ± sqrt("D"))/(2a)`
= `(-(-4) ± sqrt(60))/(2 xx 1)`
= `(4 ± sqrt(4 xx 15))/(2)`
= `(4 ± 2sqrt(15))/(2)`
= `2 ± sqrt(15)`
∴ x = `2 + sqrt(15), 2 - sqrt(15)`.
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