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D( x )
x^3-(18*x^2)+80*x = 0
x^3-(18*x^2)+80*x = 0
x^3-(18*x^2)+80*x = 0
x^3-18*x^2+80*x = 0
x^3-18*x^2+80*x = 0
x*(x^2-18*x+80) = 0
x^2-18*x+80 = 0
DELTA = (-18)^2-(1*4*80)
DELTA = 4
DELTA > 0
x = (4^(1/2)+18)/(1*2) or x = (18-4^(1/2))/(1*2)
x = 10 or x = 8
x = 0
x = 0
x in (-oo:0) U (0:8) U (8:10) U (10:+oo)
(x^2-(16*x)+64)/(x^3-(18*x^2)+80*x) = 0
(x^2-16*x+64)/(x^3-18*x^2+80*x) = 0
x^2-16*x+64 = 0
x^2-16*x+64 = 0
DELTA = (-16)^2-(1*4*64)
DELTA = 0
x = 16/(1*2)
x = 8 or x = 8
(x-8)^2 = 0
x^3-18*x^2+80*x = 0
x*(x^2-18*x+80) = 0
x^2-18*x+80 = 0
DELTA = (-18)^2-(1*4*80)
DELTA = 4
DELTA > 0
x = (4^(1/2)+18)/(1*2) or x = (18-4^(1/2))/(1*2)
x = 10 or x = 8
x*(x-8)*(x-10) = 0
((x-8)^2)/(x*(x-8)*(x-10)) = 0
x-8 = 0 // + 8
x = 8
x in { 8}
x belongs to the empty set
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