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प्रश्न
Solve the following equation by using formula :
10ax2 – 6x + 15ax – 9 = 0,a≠0
उत्तर
10ax2 – 6x + 15ax – 9 = 0
Here a = 10a, b = –(6 - 15a), c = –9
D = b2 – 4ac
= [–(6 – 15a)]2 – 4 x 10a(–9)
= 36 – 180a + 225a2 + 360a
= 36 + 180a + 225a2 = (6 + 15a)2
∴ x = `(-b ± sqrt("D"))/(2a)`
= `(-[-(6 - 15a)] ± sqrt((6 + 15a)^2))/(2 xx 10a)`
= `((6 - 15a) ± (6 + 15a))/(20a)`
∴ x1 = `(6 - 15a + 6 + 15a)/(20a)`
= `(12)/(20a)`
= `(3)/(5a)`
x2 = `(6 - 15a - 6 - 15a)/(20a)`
= `(-30a)/(20a)`
= `(-3)/(2)`
Hence x = `(3)/5a), (-3)/(2)`.
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