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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
2*x+1000/x = x+100 // - x+100
2*x-x+1000/x-100 = 0
1*x^1+1000*x^-1-100*x^0 = 0
(1*x^2-100*x^1+1000*x^0)/(x^1) = 0 // * x^2
x^1*(1*x^2-100*x^1+1000*x^0) = 0
x^1
x^2-100*x+1000 = 0
x^2-100*x+1000 = 0
DELTA = (-100)^2-(1*4*1000)
DELTA = 6000
DELTA > 0
x = (6000^(1/2)+100)/(1*2) or x = (100-6000^(1/2))/(1*2)
x = (20*15^(1/2)+100)/2 or x = (100-20*15^(1/2))/2
x in { (100-20*15^(1/2))/2, (20*15^(1/2)+100)/2}
x in { (100-20*15^(1/2))/2, (20*15^(1/2)+100)/2 }
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