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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
(x-(40/x))^2-(3*(x-(40/x)))-18 = 0
(x-40*x^-1)^2-3*(x-40*x^-1)-18 = 0
(x-40*x^-1)^2-3*(x-40*x^-1)-18 = 0
x^2-3*x+120*x^-1+1600*x^-2-80-18 = 0
x^2-3*x+120*x^-1+1600*x^-2-98 = 0
x^2-3*x+120*x^-1+1600*x^-2-98 = 0
1*x^2-3*x^1+120*x^-1+1600*x^-2-98*x^0 = 0
(1*x^4-3*x^3-98*x^2+120*x^1+1600*x^0)/(x^2) = 0 // * x^4
x^2*(1*x^4-3*x^3-98*x^2+120*x^1+1600*x^0) = 0
x^2
x^4-3*x^3-98*x^2+120*x+1600 = 0
{ 1, -1, 2, -2, 4, -4, 5, -5, 8, -8, 10, -10, 16, -16, 20, -20, 25, -25, 32, -32, 40, -40, 50, -50, 64, -64, 80, -80, 100, -100, 160, -160, 200, -200, 320, -320, 400, -400, 800, -800, 1600, -1600 }
1
x = 1
x^4-3*x^3-98*x^2+120*x+1600 = 1620
1
-1
x = -1
x^4-3*x^3-98*x^2+120*x+1600 = 1386
-1
2
x = 2
x^4-3*x^3-98*x^2+120*x+1600 = 1440
2
-2
x = -2
x^4-3*x^3-98*x^2+120*x+1600 = 1008
-2
4
x = 4
x^4-3*x^3-98*x^2+120*x+1600 = 576
4
-4
x = -4
x^4-3*x^3-98*x^2+120*x+1600 = 0
-4
x+4
x^3-7*x^2-70*x+400
x^4-3*x^3-98*x^2+120*x+1600
x+4
-x^4-4*x^3
120*x-7*x^3-98*x^2+1600
7*x^3+28*x^2
120*x-70*x^2+1600
70*x^2+280*x
400*x+1600
-400*x-1600
0
x^3-7*x^2-70*x+400 = 0
{ 1, -1, 2, -2, 4, -4, 5, -5, 8, -8, 10, -10, 16, -16, 20, -20, 25, -25, 40, -40, 50, -50, 80, -80, 100, -100, 200, -200, 400, -400 }
1
x = 1
x^3-7*x^2-70*x+400 = 324
1
-1
x = -1
x^3-7*x^2-70*x+400 = 462
-1
2
x = 2
x^3-7*x^2-70*x+400 = 240
2
-2
x = -2
x^3-7*x^2-70*x+400 = 504
-2
4
x = 4
x^3-7*x^2-70*x+400 = 72
4
-4
x = -4
x^3-7*x^2-70*x+400 = 504
-4
5
x = 5
x^3-7*x^2-70*x+400 = 0
5
x-5
x^2-2*x-80
x^3-7*x^2-70*x+400
x-5
5*x^2-x^3
400-2*x^2-70*x
2*x^2-10*x
400-80*x
80*x-400
0
x^2-2*x-80 = 0
DELTA = (-2)^2-(-80*1*4)
DELTA = 324
DELTA > 0
x = (324^(1/2)+2)/(1*2) or x = (2-324^(1/2))/(1*2)
x = 10 or x = -8
x in { -8, 10, -4, 5}
(x+8)*(x-10)*(x+4)*(x-5) = 0
(x+8)*(x-10)*(x+4)*(x-5) = 0
( x+4 )
x+4 = 0 // - 4
x = -4
( x+8 )
x+8 = 0 // - 8
x = -8
( x-10 )
x-10 = 0 // + 10
x = 10
( x-5 )
x-5 = 0 // + 5
x = 5
x in { -4, -8, 10, 5 }
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