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The number of real roots of the equation $1+\cos ^2x+\cos ^3 x – \cos^4x=5$ is equal to

1. $0$
2. $1$
3. $3$
4. $4$

recategorized | 102 views
0
Is $4$ the answer??
0

@ankitgupta.1729

Any idea how this could be done??

+1

@`JEET

To make equation satisfy, $cos^2 x +cos^3 x - cos^4 x = 4$ but $-1 \leq cosx \leq +1$. Here, we can't make sum $= 4$ for any real value of $x$. So, no real $x$ exists.

+1
Thanks.

0 real roots of the equation as the maximum value cos x can take is 1 and then LHS of equation will become 2. LHS can never become 5.
by (33 points)

+1 vote