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प्रश्न
Solve the following equation by using formula :
`(x + 1)/(x + 3) = (3x + 2)/(2x + 3)`
उत्तर
`(x + 1)/(x + 3) = (3x + 2)/(2x + 3)`
(x + 1) (2x + 3) = (3x + 2) (x + 3)
⇒ 2x2 + 3x + 2x + 3 = 3x2 + 9x + 2x + 6
⇒ 2x2 + 5x + 3 - 3x2 - 11x - 6 = 0
⇒ -x2 - 6x - 3 = 0
⇒ x2 + 6x + 3 = 0
Here a = 1, b = 6, c = 3
D = b2 - 4ac
= (6)2 - 4 x 1 x 3
= 36 - 12
= 24
∵ x = `(-b ± sqrt("D"))/(2a)`
= `(-6 ± sqrt(24))/(2 xx 1)`
= `(6 ± sqrt(4 xx 6))/(2)`
= `(-6 ± 2sqrt(6))/(2)`
= `-3 ± sqrt(6)`
∴ `x_1 = -3 + sqrt(6), x_2 = -3 - sqrt(6)`
Hence x = `-3 + sqrt(6), -3 - sqrt(6)`.
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