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D( x )
x = 0
x^2 = 0
x = 0
x = 0
x^2 = 0
x^2 = 0
1*x^2 = 0 // : 1
x^2 = 0
x = 0
x in (-oo:0) U (0:+oo)
4*(x^2+1/(x^2))-(8*(x+1/x))+3 = 0
4*(x^2+1/(x^2))-8*(x+1/x)+3 = 0
4*(x^2+x^-2)-8*(x+x^-1)+3 = 0
4*(x^2+x^-2)-8*(x+x^-1)+3 = 0
4*x^2-8*x-8*x^-1+4*x^-2+3 = 0
4*x^2-8*x-8*x^-1+4*x^-2+3 = 0
4*x^2-8*x^1-8*x^-1+4*x^-2+3*x^0 = 0
(4*x^4-8*x^3+3*x^2-8*x^1+4*x^0)/(x^2) = 0 // * x^4
x^2*(4*x^4-8*x^3+3*x^2-8*x^1+4*x^0) = 0
x^2
4*x^4-8*x^3+3*x^2-8*x+4 = 0
{ 1, -1, 2, -2, 4, -4 }
1
x = 1
4*x^4-8*x^3+3*x^2-8*x+4 = -5
1
-1
x = -1
4*x^4-8*x^3+3*x^2-8*x+4 = 27
-1
2
x = 2
4*x^4-8*x^3+3*x^2-8*x+4 = 0
2
x-2
4*x^3+3*x-2
4*x^4-8*x^3+3*x^2-8*x+4
x-2
8*x^3-4*x^4
3*x^2-8*x+4
6*x-3*x^2
4-2*x
2*x-4
0
4*x^3+3*x-2 = 0
{ 1, -1, 2, -2 }
1
x = 1
4*x^3+3*x-2 = 5
1
-1
x = -1
4*x^3+3*x-2 = -9
-1
2
x = 2
4*x^3+3*x-2 = 36
2
-2
x = -2
4*x^3+3*x-2 = -40
-2
{ 1/2, -1/2, 1/4, -1/4, -1/2, 1/2, -1/4, 1/4, 2/2, -2/2, 2/4, -2/4, -2/2, 2/2, -2/4, 2/4 }
1/2
x
1/2
4*x^3+3*x-2 = 0
1/2
x-1/2
4*x^2+2*x+4
4*x^3+3*x-2
x-1/2
2*x^2-4*x^3
2*x^2+3*x-2
x-2*x^2
4*x-2
2-4*x
0
4*x^2+2*x+4 = 0
DELTA = 2^2-(4*4*4)
DELTA = -60
DELTA < 0
x in { 2, 1/2}
(x-2)*(x-1/2) = 0
(x-2)*(x-1/2) = 0
( x-1/2 )
x-1/2 = 0 // + 1/2
x = 1/2
( x-2 )
x-2 = 0 // + 2
x = 2
x in { 1/2, 2 }
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