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Find the general solution of cos4x+6=7cos2x and also find the sum of all the solution in [0,3pi].

Find the general solution of cos4x+6=7cos2x and also find the sum of all the solution in [0,3pi].

Grade:11

1 Answers

Arun
25763 Points
4 years ago
put the formula of cos4x = 2cos22x−1
now the equation will be
2cos22x−7cos2x+5 = 0
by factorising,
(2cos2x−5)(cos2x−1)= 0
cos2x can never be 5/2 hence this is neglected
now for cos2x=1
2x = 2n\pi
hence x= n\pi
thus in [0,3\pi], solution will be 0, \pi, 2\pi, 3\pi.
and sum will be 0+\pi+2\pi+3\pi = 6\pi

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