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

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


D( x )

x < 0

x < 0

x in <0:+oo)

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

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

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

t_1 = x^(1/2)

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

t_1^2-3*t_1-1 = 0

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

DELTA = 13

DELTA > 0

t_1 = (13^(1/2)+3)/(1*2) or t_1 = (3-13^(1/2))/(1*2)

t_1 = (13^(1/2)+3)/2 or t_1 = (3-13^(1/2))/2

t_1 = (3-13^(1/2))/2

x^(1/2)-((3-13^(1/2))/2) = 0

1*x^(1/2) = (3-13^(1/2))/2 // : 1

x^(1/2) = (3-13^(1/2))/2

( (3-13^(1/2))/2 < 0 i 1/2 in (0:1) ) => x naleu017Cy do O

t_1 = (13^(1/2)+3)/2

x^(1/2)-((13^(1/2)+3)/2) = 0

1*x^(1/2) = (13^(1/2)+3)/2 // : 1

x^(1/2) = (13^(1/2)+3)/2

x^(1/2) = (13^(1/2)+3)/2 // ^ 2

x = ((13^(1/2)+3)^2)/4

x = ((13^(1/2)+3)^2)/4

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