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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
(x-(24/x))^2-(3*(x-(24/x)))-10 = 0
(x-24*x^-1)^2-3*(x-24*x^-1)-10 = 0
(x-24*x^-1)^2-3*(x-24*x^-1)-10 = 0
x^2-3*x+72*x^-1+576*x^-2-48-10 = 0
x^2-3*x+72*x^-1+576*x^-2-58 = 0
x^2-3*x+72*x^-1+576*x^-2-58 = 0
1*x^2-3*x^1+72*x^-1+576*x^-2-58*x^0 = 0
(1*x^4-3*x^3-58*x^2+72*x^1+576*x^0)/(x^2) = 0 // * x^4
x^2*(1*x^4-3*x^3-58*x^2+72*x^1+576*x^0) = 0
x^2
x^4-3*x^3-58*x^2+72*x+576 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 9, -9, 12, -12, 16, -16, 18, -18, 24, -24, 32, -32, 36, -36, 48, -48, 64, -64, 72, -72, 96, -96, 144, -144, 192, -192, 288, -288, 576, -576 }
1
x = 1
x^4-3*x^3-58*x^2+72*x+576 = 588
1
-1
x = -1
x^4-3*x^3-58*x^2+72*x+576 = 450
-1
2
x = 2
x^4-3*x^3-58*x^2+72*x+576 = 480
2
-2
x = -2
x^4-3*x^3-58*x^2+72*x+576 = 240
-2
3
x = 3
x^4-3*x^3-58*x^2+72*x+576 = 270
3
-3
x = -3
x^4-3*x^3-58*x^2+72*x+576 = 0
-3
x+3
x^3-6*x^2-40*x+192
x^4-3*x^3-58*x^2+72*x+576
x+3
-x^4-3*x^3
72*x-6*x^3-58*x^2+576
6*x^3+18*x^2
72*x-40*x^2+576
40*x^2+120*x
192*x+576
-192*x-576
0
x^3-6*x^2-40*x+192 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 16, -16, 24, -24, 32, -32, 48, -48, 64, -64, 96, -96, 192, -192 }
1
x = 1
x^3-6*x^2-40*x+192 = 147
1
-1
x = -1
x^3-6*x^2-40*x+192 = 225
-1
2
x = 2
x^3-6*x^2-40*x+192 = 96
2
-2
x = -2
x^3-6*x^2-40*x+192 = 240
-2
3
x = 3
x^3-6*x^2-40*x+192 = 45
3
-3
x = -3
x^3-6*x^2-40*x+192 = 231
-3
4
x = 4
x^3-6*x^2-40*x+192 = 0
4
x-4
x^2-2*x-48
x^3-6*x^2-40*x+192
x-4
4*x^2-x^3
192-2*x^2-40*x
2*x^2-8*x
192-48*x
48*x-192
0
x^2-2*x-48 = 0
DELTA = (-2)^2-(-48*1*4)
DELTA = 196
DELTA > 0
x = (196^(1/2)+2)/(1*2) or x = (2-196^(1/2))/(1*2)
x = 8 or x = -6
x in { -6, 8, -3, 4}
(x+6)*(x-8)*(x+3)*(x-4) = 0
(x+6)*(x-8)*(x+3)*(x-4) = 0
( x+3 )
x+3 = 0 // - 3
x = -3
( x+6 )
x+6 = 0 // - 6
x = -6
( x-4 )
x-4 = 0 // + 4
x = 4
( x-8 )
x-8 = 0 // + 8
x = 8
x in { -3, -6, 4, 8 }
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