2x^(1/2)=4x

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


D( x )

x < 0

x < 0

x in <0:+oo)

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

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

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

t_1 = x^(1/2)

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

2*t_1-4*t_1^2 = 0

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

DELTA = 4

DELTA > 0

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

t_1 = 0 or t_1 = 1/2

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 = 1/2

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

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

x^(1/2) = 1/2

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

x = 1/4

x in { 0, 1/4 }

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