it reduces to 4 cos^{3}x -4cos^{2}x+cosx-1=o
take cos x-1 common......
d arithmetic mean of d roots of d equatio n
4Cos^{3}x -4Cos^{2}x -Cos[315pie+x]=1
it reduces to 4 cos^{3}x -4cos^{2}x+cosx-1=o
take cos x-1 common......
4Cos^{3}x - 4 Cos^{2}x + Cosx = 1
let Cos x = a
4a^{3} - 4a^{2} + a = 1
4a^{3} - 4a^{2} + a - 1 = 0
(a - 1)(4a^{2} + 1) = 0
Therefore possible
a = 1
a = i/2
A.M = 1 + i /3
AM = 1/3 + i/3
when u had till here......4Cos^{3}x - 4 Cos^{2}x + Cosx = 1
then use the property.....
summation of roots=-(-4/4)=1
=> AM=1/3
But eureka when i actually solved it i got a i = √-1 in between how do i solve that
u wrote .....
a = i/2
=> cosx=i/2
writing this doesnt mean anything
i hope u unerstand.......
the question is indeed wrong...........
right question is
the arithmetic mean of d roots of the equation
4Cos^{3}x -4Cos^{2}x -Cos(π+x)=1 in interval (0,315)
solution:
proceeding as nishant sir did,we get cosx=1
=>cosx=2n.π
Since 100π<315<101π
=>cosx=2π,4π,...........100π
=>AM=2(π+2π+........50π)/50
=>AM=2*50*51*π/2*50
=>AM=51π
4Cos3x -4Cos2x -Cos[315pie+x]=1
=
4Cos^{3}x -4Cos^{2}x + Cosx-1=0
( 4 cos^{2}x +1 ) (cos x - 1) =0
the first one is not possible...
so x=(2n)π
among the options given to your brinda... you should realise that no other option will hold.. I think you must be solving a multiple choice question..
2nπ=x is the answer as range of x is [0,315] so convert 315 into radian 315×π/π≈100π so x=0,2π,4π......100π and atithimetic mean comes out to be (100π+0)/2=50π
idont understand wat ur saying bhaiyya d ans is given as 51∩ i got it can ne 1 say how it is plz
do you mean that you got the answer 51 pi?
I think that is the answer
can you tell the other options
and also can you tell the source of this question?