3x^(1/2)-4x^(1/4)=-1

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


D( x )

x < 0

x < 0

x in <0:+oo)

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

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

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

t_1 = x^(1/4)

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

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

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

DELTA = 4

DELTA > 0

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

t_1 = 1 or t_1 = 1/3

t_1 = 1/3

x^(1/4)-1/3 = 0

1*x^(1/4) = 1/3 // : 1

x^(1/4) = 1/3

x^(1/4) = 1/3 // ^ 4

x = 1/81

t_1 = 1

x^(1/4)-1 = 0

1*x^(1/4) = 1 // : 1

x^(1/4) = 1

x^(1/4) = 1 // ^ 4

x = 1

x in { 1/81, 1 }

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