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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
2*(x+1/x)^2+x+1/x-10 = 0
2*(x+x^-1)^2+x+1/x-10 = 0
(2*x*(x+x^-1)^2)/x+(x^2)/x+1/x+(-10*x)/x = 0
2*x*(x+x^-1)^2+x^2-10*x+1 = 0
2*x^3+x^2+4*x-10*x+2*x^-1+1 = 0
2*x^3+x^2-6*x+2*x^-1+1 = 0
2*x^3+x^2-6*x+2*x^-1+1 = 0
2*x^3+1*x^2-6*x^1+2*x^-1+1*x^0 = 0
(2*x^4+1*x^3-6*x^2+1*x^1+2*x^0)/(x^1) = 0 // * x^2
x^1*(2*x^4+1*x^3-6*x^2+1*x^1+2*x^0) = 0
x^1
2*x^4+x^3-6*x^2+x+2 = 0
{ 1, -1, 2, -2 }
1
x = 1
2*x^4+x^3-6*x^2+x+2 = 0
1
x-1
2*x^3+3*x^2-3*x-2
2*x^4+x^3-6*x^2+x+2
x-1
2*x^3-2*x^4
3*x^3-6*x^2+x+2
3*x^2-3*x^3
x-3*x^2+2
3*x^2-3*x
2-2*x
2*x-2
0
2*x^3+3*x^2-3*x-2 = 0
{ 1, -1, 2, -2 }
1
x = 1
2*x^3+3*x^2-3*x-2 = 0
1
x-1
2*x^2+5*x+2
2*x^3+3*x^2-3*x-2
x-1
2*x^2-2*x^3
5*x^2-3*x-2
5*x-5*x^2
2*x-2
2-2*x
0
2*x^2+5*x+2 = 0
DELTA = 5^2-(2*2*4)
DELTA = 9
DELTA > 0
x = (9^(1/2)-5)/(2*2) or x = (-9^(1/2)-5)/(2*2)
x = -1/2 or x = -2
x in { -2, -1/2, 1, 1}
(x+2)*(x+1/2)*(x-1)^2 = 0
((x+2)*(x+1/2)*(x-1)^2)/x = 0
((x+2)*(x+1/2)*(x-1)^2)/x = 0 // * x
(x+2)*(x+1/2)*(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-1 )
x-1 = 0 // + 1
x = 1
x in { -1/2, -2, 1, 1 }
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