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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
(1/x-5)^2-(x-5)^2 = 0
(x^-1-5)^2-1*(x-5)^2 = 0
(x^-1-5)^2-1*(x-5)^2 = 0
10*x-x^2-10*x^-1+x^-2 = 0
10*x-x^2-10*x^-1+x^-2 = 0
x*(x^-3-x-10*x^-2+10) = 0
1*x^-3-1*x^1-10*x^-2+10*x^0 = 0
(10*x^3-1*x^4-10*x^1+1*x^0)/(x^3) = 0 // * x^6
x^3*(10*x^3-1*x^4-10*x^1+1*x^0) = 0
x^3
10*x^3-x^4-10*x+1 = 0
{ 1, -1 }
1
x = 1
10*x^3-x^4-10*x+1 = 0
1
x-1
9*x^2-x^3+9*x-1
10*x^3-x^4-10*x+1
x-1
x^4-x^3
9*x^3-10*x+1
9*x^2-9*x^3
9*x^2-10*x+1
9*x-9*x^2
1-x
x-1
0
9*x^2-x^3+9*x-1 = 0
{ 1, -1 }
1
x = 1
9*x^2-x^3+9*x-1 = 16
1
-1
x = -1
9*x^2-x^3+9*x-1 = 0
-1
x+1
10*x-x^2-1
9*x^2-x^3+9*x-1
x+1
x^3+x^2
10*x^2+9*x-1
-10*x^2-10*x
-x-1
x+1
0
10*x-x^2-1 = 0
DELTA = 10^2-(-1*(-1)*4)
DELTA = 96
DELTA > 0
x = (96^(1/2)-10)/(-1*2) or x = (-96^(1/2)-10)/(-1*2)
x = (4*6^(1/2)-10)/(-2) or x = (-4*6^(1/2)-10)/(-2)
x in { (4*6^(1/2)-10)/(-2), (-4*6^(1/2)-10)/(-2), 1, -1}
x*(x-((4*6^(1/2)-10)/(-2)))*(x-((-4*6^(1/2)-10)/(-2)))*(x-1)*(x+1) = 0
x*(x-((4*6^(1/2)-10)/(-2)))*(x-((-4*6^(1/2)-10)/(-2)))*(x-1)*(x+1) = 0
( x+1 )
x+1 = 0 // - 1
x = -1
( x-((-4*6^(1/2)-10)/(-2)) )
x-((-4*6^(1/2)-10)/(-2)) = 0 // + (-4*6^(1/2)-10)/(-2)
x = (-4*6^(1/2)-10)/(-2)
( x-((4*6^(1/2)-10)/(-2)) )
x-((4*6^(1/2)-10)/(-2)) = 0 // + (4*6^(1/2)-10)/(-2)
x = (4*6^(1/2)-10)/(-2)
( x-1 )
x-1 = 0 // + 1
x = 1
( x )
x = 0
x in { 0}
x in { -1, (-4*6^(1/2)-10)/(-2), (4*6^(1/2)-10)/(-2), 1 }
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