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the number of values of x in [0,5π],satisfying 3cos2x-10cosx=7=0 are i)4 ii)8 iii)6 iv)10

the number of values of x in [0,5π],satisfying 3cos2x-10cosx=7=0 are i)4 ii)8 iii)6 iv)10


 

Grade:12

1 Answers

Harsh Bajaj
30 Points
10 years ago

Hey Shaoni Chakravarty

Firstly I think you were asking  3cos2x - 10cosx + 7 = 0

(cos2x = 2cos²x - 1)

3(2cos²x-1)-10cosx+7=0

6cos²x-3-10cosx+7=0

6cos²x-10cosx+4=0

6cosx(cosx-1)-4(cosx-1)=0

(6cosx-4)(cosx-1)=0

cosx  = 2/3

x=59,2∏+59,4∏+59

cosx=1

x=0,2∏,4∏

Therefore the expression totally has 6 values option (iii)

Hope this helped you so please can you approve it
thank you

 

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