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The number of values of x in [0, 5pie] satisfying the equation 3cos2x-10cosx+7=0 is:

1 Answer

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Best answer

(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=59,2π+59,4π+59  

cosx=1  

x=0,2π,4π 

Therefore the expression totally has 6 values option (iii)

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