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x-3-x-c-0-lt-c-lt-2-3-3-Find-x-




Question Number 139103 by ajfour last updated on 22/Apr/21
x^3 −x=c   ;  0<c<(2/(3(√3))) . Find x.
x3x=c;0<c<233.Findx.
Commented by ajfour last updated on 24/Apr/21
Answered by mr W last updated on 23/Apr/21
sin 3θ=sin θ(3−4 sin^2  θ)  (2/( 3(√3)))sin 3θ=((2sin θ)/( (√3)))(1−(((2sin θ)/( (√3))))^2 )  −c=x(1−x^2 )  ⇒(2/(3(√3)))sin 3θ=−c  ⇒θ=−(1/3)(sin^(−1) ((3(√3)c)/2)+2kπ)  ⇒x=((2 sin θ)/( (√3)))=−(2/( (√3))) sin ((1/3)sin^(−1) ((3(√3)c)/2)+((2kπ)/3))
sin3θ=sinθ(34sin2θ)233sin3θ=2sinθ3(1(2sinθ3)2)c=x(1x2)233sin3θ=cθ=13(sin133c2+2kπ)x=2sinθ3=23sin(13sin133c2+2kπ3)
Commented by mr W last updated on 24/Apr/21
i don′t know any other methods for  the solution.
idontknowanyothermethodsforthesolution.

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