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D( x )
x^2 = 0
x^2 = 0
x^2 = 0
1*x^2 = 0 // : 1
x^2 = 0
x = 0
x in (-oo:0) U (0:+oo)
x^2-(10*x)-(16/(x^2))+25 = 0
x^2-10*x-16*x^-2+25 = 0
1*x^2-10*x^1-16*x^-2+25*x^0 = 0
(1*x^4-10*x^3+25*x^2-16*x^0)/(x^2) = 0 // * x^4
x^2*(1*x^4-10*x^3+25*x^2-16*x^0) = 0
x^2
x^4-10*x^3+25*x^2-16 = 0
{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16 }
1
x = 1
x^4-10*x^3+25*x^2-16 = 0
1
x-1
x^3-9*x^2+16*x+16
x^4-10*x^3+25*x^2-16
x-1
x^3-x^4
25*x^2-9*x^3-16
9*x^3-9*x^2
16*x^2-16
16*x-16*x^2
16*x-16
16-16*x
0
x^3-9*x^2+16*x+16 = 0
{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16 }
1
x = 1
x^3-9*x^2+16*x+16 = 24
1
-1
x = -1
x^3-9*x^2+16*x+16 = -10
-1
2
x = 2
x^3-9*x^2+16*x+16 = 20
2
-2
x = -2
x^3-9*x^2+16*x+16 = -60
-2
4
x = 4
x^3-9*x^2+16*x+16 = 0
4
x-4
x^2-5*x-4
x^3-9*x^2+16*x+16
x-4
4*x^2-x^3
16*x-5*x^2+16
5*x^2-20*x
16-4*x
4*x-16
0
x^2-5*x-4 = 0
DELTA = (-5)^2-(-4*1*4)
DELTA = 41
DELTA > 0
x = (41^(1/2)+5)/(1*2) or x = (5-41^(1/2))/(1*2)
x = (41^(1/2)+5)/2 or x = (5-41^(1/2))/2
x in { (5-41^(1/2))/2, (41^(1/2)+5)/2, 1, 4}
x in { (5-41^(1/2))/2, (41^(1/2)+5)/2, 1, 4 }
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