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

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


D( x )

2*x < 0

2*x < 0

2*x < 0

2*x+0 < 0 // - 0

2*x < 0 // : 2

x < 0/2

x < 0

x in <0:+oo)

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

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

x-x^(1/2) = 0

t_1 = x^(1/2)

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

t_1^2-t_1 = 0

DELTA = (-1)^2-(0*1*4)

DELTA = 1

DELTA > 0

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

t_1 = 1 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 = 1

x^(1/2)-1 = 0

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

x^(1/2) = 1

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

x = 1

x in { 0, 1 }

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