4x^(1/2)-9x^(1/4)+3=0

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Solution for 4x^(1/2)-9x^(1/4)+3=0 equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

4*x^(1/2)-(9*x^(1/4))+3 = 0

4*x^(1/2)-9*x^(1/4)+3 = 0

t_1 = x^(1/4)

4*t_1^2-9*t_1^1+3 = 0

4*t_1^2-9*t_1+3 = 0

DELTA = (-9)^2-(3*4*4)

DELTA = 33

DELTA > 0

t_1 = (33^(1/2)+9)/(2*4) or t_1 = (9-33^(1/2))/(2*4)

t_1 = (33^(1/2)+9)/8 or t_1 = (9-33^(1/2))/8

t_1 = (9-33^(1/2))/8

x^(1/4)-((9-33^(1/2))/8) = 0

1*x^(1/4) = (9-33^(1/2))/8 // : 1

x^(1/4) = (9-33^(1/2))/8

x^(1/4) = (9-33^(1/2))/8 // ^ 4

x = ((9-33^(1/2))^4)/4096

t_1 = (33^(1/2)+9)/8

x^(1/4)-((33^(1/2)+9)/8) = 0

1*x^(1/4) = (33^(1/2)+9)/8 // : 1

x^(1/4) = (33^(1/2)+9)/8

x^(1/4) = (33^(1/2)+9)/8 // ^ 4

x = ((33^(1/2)+9)^4)/4096

x in { ((9-33^(1/2))^4)/4096, ((33^(1/2)+9)^4)/4096 }

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