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

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Solution for x-(8x^(1/2))+4=0 equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

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

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

t_1 = x^(1/2)

1*t_1^2-8*t_1^1+4 = 0

t_1^2-8*t_1+4 = 0

DELTA = (-8)^2-(1*4*4)

DELTA = 48

DELTA > 0

t_1 = (48^(1/2)+8)/(1*2) or t_1 = (8-48^(1/2))/(1*2)

t_1 = (4*3^(1/2)+8)/2 or t_1 = (8-4*3^(1/2))/2

t_1 = (8-4*3^(1/2))/2

x^(1/2)-((8-4*3^(1/2))/2) = 0

1*x^(1/2) = (8-4*3^(1/2))/2 // : 1

x^(1/2) = (8-4*3^(1/2))/2

x^(1/2) = (8-4*3^(1/2))/2 // ^ 2

x = ((8-4*3^(1/2))^2)/4

t_1 = (4*3^(1/2)+8)/2

x^(1/2)-((4*3^(1/2)+8)/2) = 0

1*x^(1/2) = (4*3^(1/2)+8)/2 // : 1

x^(1/2) = (4*3^(1/2)+8)/2

x^(1/2) = (4*3^(1/2)+8)/2 // ^ 2

x = ((4*3^(1/2)+8)^2)/4

x in { ((8-4*3^(1/2))^2)/4, ((4*3^(1/2)+8)^2)/4 }

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