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प्रश्न
Solve the following equation by using formula :
`sqrt(3)x^2 + 10x - 8sqrt(3)` = 0
उत्तर
`sqrt(3)x^2 + 10x - 8sqrt(3)` = 0
Here `a = sqrt(3), b = 10, c = -8sqrt(3)`
D = b2 - 4ac
= `(10)^2 - 4 xx sqrt(3) xx (-8sqrt(3))`
= 100 + 96
= 196
∵ x = `(-b ± sqrt("D"))/(2a)`
= `(-10 ± sqrt(196))/(2 xx sqrt(3))`
= `(-10 ± 14)/(2sqrt(3)`
∴ x1 = `(-10 + 14)/(2sqrt(3)`
= `(4)/(2sqrt(3)`
= `(2 xx sqrt(3))/(sqrt(3) xx sqrt(3)`
= `(2sqrt(3))/(3)`
x2 = `(-10 - 14)/(2sqrt(3)`
= `(-24)/(2sqrt(3)`
= `(-12 xx sqrt(3))/(sqrt(3) xx sqrt(3)`
= `(-12sqrt(3))/(3)`
= `-4sqrt(3)`
Hence x = `(2sqrt(3))/(3), -4sqrt(3)`.
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