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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
2*x^2-(5/x) = 51 // - 51
2*x^2-(5/x)-51 = 0
2*x^2-5*x^-1-51 = 0
2*x^2-5*x^-1-51*x^0 = 0
(2*x^3-51*x^1-5*x^0)/(x^1) = 0 // * x^2
x^1*(2*x^3-51*x^1-5*x^0) = 0
x^1
2*x^3-51*x-5 = 0
{ 1, -1, 5, -5 }
1
x = 1
2*x^3-51*x-5 = -54
1
-1
x = -1
2*x^3-51*x-5 = 44
-1
5
x = 5
2*x^3-51*x-5 = -10
5
-5
x = -5
2*x^3-51*x-5 = 0
-5
x+5
2*x^2-10*x-1
2*x^3-51*x-5
x+5
-2*x^3-10*x^2
-10*x^2-51*x-5
10*x^2+50*x
-x-5
x+5
0
2*x^2-10*x-1 = 0
DELTA = (-10)^2-(-1*2*4)
DELTA = 108
DELTA > 0
x = (108^(1/2)+10)/(2*2) or x = (10-108^(1/2))/(2*2)
x = (6*3^(1/2)+10)/4 or x = (10-6*3^(1/2))/4
x in { (10-6*3^(1/2))/4, (6*3^(1/2)+10)/4, -5}
x in { (10-6*3^(1/2))/4, (6*3^(1/2)+10)/4, -5 }
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