8x^2=x^(1/2)

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Solution for 8x^2=x^(1/2) equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

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

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

t_1 = x^(1/2)

8*t_1^4-1*t_1^1 = 0

8*t_1^4-t_1 = 0

t_1*(8*t_1^3-1) = 0

8*t_1^3 = 1 // : 8

t_1^3 = 1/8

t_1^3 = 1/8 // ^ 1/3

t_1 = 1/2

t_1 = 0

t_1 = 0

t_1 = 1/2

x^(1/2)-1/2 = 0

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

x^(1/2) = 1/2

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

x = 1/4

t_1 = 0

x^(1/2)+0 = 0

x^(1/2) = 0

1*x^(1/2) = 0 // : 1

x^(1/2) = 0

x = 0

x in { 1/4, 0 }

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