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D( x )
x-3 = 0
x-3 = 0
x-3 = 0
x-3 = 0 // + 3
x = 3
x in (-oo:3) U (3:+oo)
(x^5-(15*x^4)+90*x^3-(270*x^2)+405*x-243)/(x-3) = 0
(x^5-15*x^4+90*x^3-270*x^2+405*x-243)/(x-3) = 0
x^5-15*x^4+90*x^3-270*x^2+405*x-243 = 0
x^5-15*x^4+90*x^3-270*x^2+405*x-243 = 0
{ 1, -1, 3, -3, 9, -9, 27, -27, 81, -81, 243, -243 }
1
x = 1
x^5-15*x^4+90*x^3-270*x^2+405*x-243 = -32
1
-1
x = -1
x^5-15*x^4+90*x^3-270*x^2+405*x-243 = -1024
-1
3
x = 3
x^5-15*x^4+90*x^3-270*x^2+405*x-243 = 0
3
x-3
x^4-12*x^3+54*x^2-108*x+81
x^5-15*x^4+90*x^3-270*x^2+405*x-243
x-3
3*x^4-x^5
90*x^3-12*x^4-270*x^2+405*x-243
12*x^4-36*x^3
54*x^3-270*x^2+405*x-243
162*x^2-54*x^3
405*x-108*x^2-243
108*x^2-324*x
81*x-243
243-81*x
0
x^4-12*x^3+54*x^2-108*x+81 = 0
{ 1, -1, 3, -3, 9, -9, 27, -27, 81, -81 }
1
x = 1
x^4-12*x^3+54*x^2-108*x+81 = 16
1
-1
x = -1
x^4-12*x^3+54*x^2-108*x+81 = 256
-1
3
x = 3
x^4-12*x^3+54*x^2-108*x+81 = 0
3
x-3
x^3-9*x^2+27*x-27
x^4-12*x^3+54*x^2-108*x+81
x-3
3*x^3-x^4
54*x^2-9*x^3-108*x+81
9*x^3-27*x^2
27*x^2-108*x+81
81*x-27*x^2
81-27*x
27*x-81
0
x^3-9*x^2+27*x-27 = 0
{ 1, -1, 3, -3, 9, -9, 27, -27 }
1
x = 1
x^3-9*x^2+27*x-27 = -8
1
-1
x = -1
x^3-9*x^2+27*x-27 = -64
-1
3
x = 3
x^3-9*x^2+27*x-27 = 0
3
x-3
x^2-6*x+9
x^3-9*x^2+27*x-27
x-3
3*x^2-x^3
27*x-6*x^2-27
6*x^2-18*x
9*x-27
27-9*x
0
x^2-6*x+9 = 0
DELTA = (-6)^2-(1*4*9)
DELTA = 0
x = 6/(1*2)
x = 3 or x = 3
x in { 3, 3, 3, 3, 3}
(x-3)^5 = 0
(x-3)^4 = 0
x-3 = 0 // + 3
x = 3
x in { 3}
x belongs to the empty set
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