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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
(1/x-(x/2))*(2/x-x) = 1/2 // - 1/2
(1/x-(x/2))*(2/x-x)-(1/2) = 0
(1/x-(x/2))*(2/x-x)-1/2 = 0
(x^-1-1/2*x)*(2*x^-1-x)-1/2 = 0
(2*(x^-1-1/2*x)*(2*x^-1-x))/2-1/2 = 0
2*(x^-1-1/2*x)*(2*x^-1-x)-1 = 0
x^2+4*x^-2-5 = 0
x^2+4*x^-2-5 = 0
1*x^2+4*x^-2-5*x^0 = 0
(1*x^4-5*x^2+4*x^0)/(x^2) = 0 // * x^4
x^2*(1*x^4-5*x^2+4*x^0) = 0
x^2
x^4-5*x^2+4 = 0
{ 1, -1, 2, -2, 4, -4 }
1
x = 1
x^4-5*x^2+4 = 0
1
x-1
x^3+x^2-4*x-4
x^4-5*x^2+4
x-1
x^3-x^4
x^3-5*x^2+4
x^2-x^3
4-4*x^2
4*x^2-4*x
4-4*x
4*x-4
0
x^3+x^2-4*x-4 = 0
{ 1, -1, 2, -2, 4, -4 }
1
x = 1
x^3+x^2-4*x-4 = -6
1
-1
x = -1
x^3+x^2-4*x-4 = 0
-1
x+1
x^2-4
x^3+x^2-4*x-4
x+1
-x^3-x^2
-4*x-4
4*x+4
0
x^2-4 = 0
DELTA = 0^2-(-4*1*4)
DELTA = 16
DELTA > 0
x = (16^(1/2)+0)/(1*2) or x = (0-16^(1/2))/(1*2)
x = 2 or x = -2
x in { -2, 2, 1, -1}
(x+2)*(x-2)*(x-1)*(x+1) = 0
((x+2)*(x-2)*(x-1)*(x+1))/2 = 0
((x+2)*(x-2)*(x-1)*(x+1))/2 = 0 // * 2
(x+2)*(x-2)*(x-1)*(x+1) = 0
( x+1 )
x+1 = 0 // - 1
x = -1
( x+2 )
x+2 = 0 // - 2
x = -2
( x-1 )
x-1 = 0 // + 1
x = 1
( x-2 )
x-2 = 0 // + 2
x = 2
x in { -1, -2, 1, 2 }
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