3x=4x^(1/2)

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


D( x )

x < 0

x < 0

x in <0:+oo)

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

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

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

t_1 = x^(1/2)

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

3*t_1^2-4*t_1 = 0

DELTA = (-4)^2-(0*3*4)

DELTA = 16

DELTA > 0

t_1 = (16^(1/2)+4)/(2*3) or t_1 = (4-16^(1/2))/(2*3)

t_1 = 4/3 or t_1 = 0

t_1 = 0

x^(1/2)+0 = 0

x^(1/2) = 0

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

x^(1/2) = 0

x = 0

t_1 = 4/3

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

1*x^(1/2) = 4/3 // : 1

x^(1/2) = 4/3

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

x = 16/9

x in { 0, 16/9 }

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