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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
(x-(8/x))^2-(5*(x-(8/x)))-14 = 0
(x-8*x^-1)^2-5*(x-8*x^-1)-14 = 0
(x-8*x^-1)^2-5*(x-8*x^-1)-14 = 0
x^2-5*x+40*x^-1+64*x^-2-16-14 = 0
x^2-5*x+40*x^-1+64*x^-2-30 = 0
x^2-5*x+40*x^-1+64*x^-2-30 = 0
1*x^2-5*x^1+40*x^-1+64*x^-2-30*x^0 = 0
(1*x^4-5*x^3-30*x^2+40*x^1+64*x^0)/(x^2) = 0 // * x^4
x^2*(1*x^4-5*x^3-30*x^2+40*x^1+64*x^0) = 0
x^2
x^4-5*x^3-30*x^2+40*x+64 = 0
{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64 }
1
x = 1
x^4-5*x^3-30*x^2+40*x+64 = 70
1
-1
x = -1
x^4-5*x^3-30*x^2+40*x+64 = 0
-1
x+1
x^3-6*x^2-24*x+64
x^4-5*x^3-30*x^2+40*x+64
x+1
-x^4-x^3
40*x-6*x^3-30*x^2+64
6*x^3+6*x^2
40*x-24*x^2+64
24*x^2+24*x
64*x+64
-64*x-64
0
x^3-6*x^2-24*x+64 = 0
{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64 }
1
x = 1
x^3-6*x^2-24*x+64 = 35
1
-1
x = -1
x^3-6*x^2-24*x+64 = 81
-1
2
x = 2
x^3-6*x^2-24*x+64 = 0
2
x-2
x^2-4*x-32
x^3-6*x^2-24*x+64
x-2
2*x^2-x^3
64-4*x^2-24*x
4*x^2-8*x
64-32*x
32*x-64
0
x^2-4*x-32 = 0
DELTA = (-4)^2-(-32*1*4)
DELTA = 144
DELTA > 0
x = (144^(1/2)+4)/(1*2) or x = (4-144^(1/2))/(1*2)
x = 8 or x = -4
x in { -4, 8, -1, 2}
(x+4)*(x-8)*(x+1)*(x-2) = 0
(x+4)*(x-8)*(x+1)*(x-2) = 0
( x+1 )
x+1 = 0 // - 1
x = -1
( x+4 )
x+4 = 0 // - 4
x = -4
( x-2 )
x-2 = 0 // + 2
x = 2
( x-8 )
x-8 = 0 // + 8
x = 8
x in { -1, -4, 2, 8 }
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