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D( x )
x < 0
x < 0
x in <0:+oo)
x^(1/4)-(3*x^(1/6)) = 3*x^(1/12)-9 // - 3*x^(1/12)-9
x^(1/4)-(3*x^(1/6))-(3*x^(1/12))+9 = 0
x^(1/4)-3*x^(1/6)-3*x^(1/12)+9 = 0
t_1 = x^(1/12)
1*t_1^3-3*t_1^2-3*t_1^1+9 = 0
t_1^3-3*t_1^2-3*t_1+9 = 0
{ 1, -1, 3, -3, 9, -9 }
1
t_1 = 1
t_1^3-3*t_1^2-3*t_1+9 = 4
1
-1
t_1 = -1
t_1^3-3*t_1^2-3*t_1+9 = 8
-1
3
t_1 = 3
t_1^3-3*t_1^2-3*t_1+9 = 0
3
t_1-3
t_1^2-3
t_1^3-3*t_1^2-3*t_1+9
t_1-3
3*t_1^2-t_1^3
9-3*t_1
3*t_1-9
0
t_1^2-3 = 0
DELTA = 0^2-(-3*1*4)
DELTA = 12
DELTA > 0
t_1 = (12^(1/2)+0)/(1*2) or t_1 = (0-12^(1/2))/(1*2)
t_1 = 3^(1/2) or t_1 = -3^(1/2)
t_1 in { -3^(1/2), 3^(1/2), 3}
t_1 = -3^(1/2)
x^(1/12)+3^(1/2) = 0
1*x^(1/12) = -3^(1/2) // : 1
x^(1/12) = -3^(1/2)
( -3^(1/2) < 0 i 1/12 in (0:1) ) => x należy do O
t_1 = 3^(1/2)
x^(1/12)-3^(1/2) = 0
1*x^(1/12) = 3^(1/2) // : 1
x^(1/12) = 3^(1/2)
x^(1/12) = 3^(1/2) // ^ 12
x = 729
t_1 = 3
x^(1/12)-3 = 0
1*x^(1/12) = 3 // : 1
x^(1/12) = 3
x^(1/12) = 3 // ^ 12
x = 531441
x in { 729, 531441 }
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