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

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


D( x )

x < 0

x < 0

x in <0:+oo)

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

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

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

t_1 = x^(1/2)

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

t_1^2-3*t_1+2 = 0

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

DELTA = 1

DELTA > 0

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

t_1 = 2 or t_1 = 1

t_1 = 1

x^(1/2)-1 = 0

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

x^(1/2) = 1

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

x = 1

t_1 = 2

x^(1/2)-2 = 0

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

x^(1/2) = 2

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

x = 4

x in { 1, 4 }

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