(4x)^(2/3)-(31x)^(1/3)-8=0

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Solution for (4x)^(2/3)-(31x)^(1/3)-8=0 equation: 


x in (-oo:+oo)

(4*x)^(2/3)-(31*x)^(1/3)-8 = 0

4^(2/3)*x^(2/3)-x^(1/3)-8 = 0

t_1 = x^(1/3)

4^(2/3)*t_1^2-1*t_1^1-8 = 0

4^(2/3)*t_1^2-t_1-8 = 0

DELTA = (-1)^2-(-8*4*4^(2/3))

DELTA = 32*4^(2/3)+1

DELTA = 81.63494688

DELTA > 0

t_1 = ((32*4^(2/3)+1)^(1/2)+1)/(2*4^(2/3)) or t_1 = (1-(32*4^(2/3)+1)^(1/2))/(2*4^(2/3))

t_1 = (1-(32*4^(2/3)+1)^(1/2))/(2*4^(2/3))

x^(1/3)-((1-(32*4^(2/3)+1)^(1/2))/(2*4^(2/3))) = 0

1*x^(1/3) = (1-(32*4^(2/3)+1)^(1/2))/(2*4^(2/3)) // : 1

x^(1/3) = (1-(32*4^(2/3)+1)^(1/2))/(2*4^(2/3))

( (1-(32*4^(2/3)+1)^(1/2))/(2*4^(2/3)) < 0 i 1/3 in (0:1) ) => x naleu017Cy do O

t_1 = ((32*4^(2/3)+1)^(1/2)+1)/(2*4^(2/3))

x^(1/3)-(((32*4^(2/3)+1)^(1/2)+1)/(2*4^(2/3))) = 0

1*x^(1/3) = ((32*4^(2/3)+1)^(1/2)+1)/(2*4^(2/3)) // : 1

x^(1/3) = ((32*4^(2/3)+1)^(1/2)+1)/(2*4^(2/3))

x^(1/3) = ((32*4^(2/3)+1)^(1/2)+1)/(2*4^(2/3)) // ^ 3

x = (((32*4^(2/3)+1)^(1/2)+1)^3)/128

x = (((32*4^(2/3)+1)^(1/2)+1)^3)/128

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