x-8x^(1/2)+11=0

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Solution for x-8x^(1/2)+11=0 equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

x-(8*x^(1/2))+11 = 0

x-8*x^(1/2)+11 = 0

t_1 = x^(1/2)

1*t_1^2-8*t_1^1+11 = 0

t_1^2-8*t_1+11 = 0

DELTA = (-8)^2-(1*4*11)

DELTA = 20

DELTA > 0

t_1 = (20^(1/2)+8)/(1*2) or t_1 = (8-20^(1/2))/(1*2)

t_1 = (2*5^(1/2)+8)/2 or t_1 = (8-2*5^(1/2))/2

t_1 = (8-2*5^(1/2))/2

x^(1/2)-((8-2*5^(1/2))/2) = 0

1*x^(1/2) = (8-2*5^(1/2))/2 // : 1

x^(1/2) = (8-2*5^(1/2))/2

x^(1/2) = (8-2*5^(1/2))/2 // ^ 2

x = ((8-2*5^(1/2))^2)/4

t_1 = (2*5^(1/2)+8)/2

x^(1/2)-((2*5^(1/2)+8)/2) = 0

1*x^(1/2) = (2*5^(1/2)+8)/2 // : 1

x^(1/2) = (2*5^(1/2)+8)/2

x^(1/2) = (2*5^(1/2)+8)/2 // ^ 2

x = ((2*5^(1/2)+8)^2)/4

x in { ((8-2*5^(1/2))^2)/4, ((2*5^(1/2)+8)^2)/4 }

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