x-4-(9x)^(1/2)

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Solution for x-4-(9x)^(1/2) equation: 


D( x )

9*x < 0

9*x < 0

9*x < 0

9*x+0 < 0 // - 0

9*x < 0 // : 9

x < 0/9

x < 0

x in <0:+oo)

x-(9*x)^(1/2)-4 = 0

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

t_1 = x^(1/2)

1*t_1^2-3*t_1^1-4 = 0

t_1^2-3*t_1-4 = 0

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

DELTA = 25

DELTA > 0

t_1 = (25^(1/2)+3)/(1*2) or t_1 = (3-25^(1/2))/(1*2)

t_1 = 4 or t_1 = -1

t_1 = -1

x^(1/2)+1 = 0

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

x^(1/2) = -1

( -1 < 0 i 1/2 in (0:1) ) => x należy do O

t_1 = 4

x^(1/2)-4 = 0

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

x^(1/2) = 4

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

x = 16

x = 16

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