X^(1/3)-2X^(1/6)-5

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Solution for X^(1/3)-2X^(1/6)-5 equation: 


D( X )

X < 0

X < 0

X in <0:+oo)

X^(1/3)-(2*X^(1/6))-5 = 0

X^(1/3)-2*X^(1/6)-5 = 0

t_1 = X^(1/6)

1*t_1^2-2*t_1^1-5 = 0

t_1^2-2*t_1-5 = 0

DELTA = (-2)^2-(-5*1*4)

DELTA = 24

DELTA > 0

t_1 = (24^(1/2)+2)/(1*2) or t_1 = (2-24^(1/2))/(1*2)

t_1 = (2*6^(1/2)+2)/2 or t_1 = (2-2*6^(1/2))/2

t_1 = (2-2*6^(1/2))/2

X^(1/6)-((2-2*6^(1/2))/2) = 0

1*X^(1/6) = (2-2*6^(1/2))/2 // : 1

X^(1/6) = (2-2*6^(1/2))/2

( (2-2*6^(1/2))/2 < 0 i 1/6 in (0:1) ) => X należy do O

t_1 = (2*6^(1/2)+2)/2

X^(1/6)-((2*6^(1/2)+2)/2) = 0

1*X^(1/6) = (2*6^(1/2)+2)/2 // : 1

X^(1/6) = (2*6^(1/2)+2)/2

X^(1/6) = (2*6^(1/2)+2)/2 // ^ 6

X = ((2*6^(1/2)+2)^6)/64

X = ((2*6^(1/2)+2)^6)/64

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