x^(4/3)-10x^(2/3)+16=0

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Solution for x^(4/3)-10x^(2/3)+16=0 equation: 


x in (-oo:+oo)

x^(4/3)-(10*x^(2/3))+16 = 0

x^(4/3)-10*x^(2/3)+16 = 0

t_1 = x^(2/3)

1*t_1^2-10*t_1^1+16 = 0

t_1^2-10*t_1+16 = 0

DELTA = (-10)^2-(1*4*16)

DELTA = 36

DELTA > 0

t_1 = (36^(1/2)+10)/(1*2) or t_1 = (10-36^(1/2))/(1*2)

t_1 = 8 or t_1 = 2

t_1 = 2

x^(2/3)-2 = 0

1*x^(2/3) = 2 // : 1

x^(2/3) = 2

x^(2/3) = 2 // ^ 3

x^2 = 8 // ^ 1/2

abs(x) = 2*2^(1/2)

x = 2*2^(1/2) or x = -(2*2^(1/2))

t_1 = 8

x^(2/3)-8 = 0

1*x^(2/3) = 8 // : 1

x^(2/3) = 8

x^(2/3) = 8 // ^ 3

x^2 = 512 // ^ 1/2

abs(x) = 16*2^(1/2)

x = 16*2^(1/2) or x = -(16*2^(1/2))

x in { 2*2^(1/2), -(2*2^(1/2)), 16*2^(1/2), -(16*2^(1/2)) }

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