Question

Solve the following equation by using formula :

`(2x + 5)/(3x + 4) = (x + 1)/(x + 3)`

Answer 1

`(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)`.