What is the general solution for cos^4(x)+cos^3(x)-2=0 ?

The general solution for cos^4(x)+cos^3(x)-2=0 is x=2pin

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cos^4(x)+cos^3(x)-2=0

cos^{4} (x) + cos^{3} (x) - 2 = 0

x = 2 πn

Solution steps

cos^{4} (x) + cos^{3} (x) - 2 = 0

Solve by substitution

cos (x) = 1, cos (x) \approx - 1.54368 \dots

cos (x) = 1 : x = 2 πn

cos (x) = - 1.54368 \dots :

No Solution

Combine all the solutions

x = 2 πn

tan^{2} (x) = \frac{1}{cos ( x ) + 1}

\frac{sin ^{2} ( x ) - 2 cos ( x ) + 1}{4} = 0

cos^{2} (x) + cos^{4} (x) + cos^{6} (x) = 0

sin (x) = \frac{- 1}{4}

sin^{4} (x) - sin^{2} (x) = 0

What is the general solution for cos^4(x)+cos^3(x)-2=0 ?
The general solution for cos^4(x)+cos^3(x)-2=0 is x=2pin