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D( k )
2*k+8 = 0
k+4 = 0
2*k+8 = 0
2*k+8 = 0
2*k+8 = 0 // - 8
2*k = -8 // : 2
k = -8/2
k = -4
k+4 = 0
k+4 = 0
k+4 = 0 // - 4
k = -4
k in (-oo:-4) U (-4:+oo)
1/(2*k+8)+1/2 = (k^2+k-20)/(k+4) // - (k^2+k-20)/(k+4)
1/(2*k+8)-((k^2+k-20)/(k+4))+1/2 = 0
1/(2*k+8)+(-1*(k^2+k-20))/(k+4)+1/2 = 0
(1*2*(k+4))/(2*(2*k+8)*(k+4))+(-1*2*(k^2+k-20)*(2*k+8))/(2*(2*k+8)*(k+4))+(1*(2*k+8)*(k+4))/(2*(2*k+8)*(k+4)) = 0
1*2*(k+4)-1*2*(k^2+k-20)*(2*k+8)+1*(2*k+8)*(k+4) = 0
2*k^2-4*k^3-20*k^2+66*k+16*k+32+328 = 0
82*k-4*k^3-18*k^2+360 = 0
82*k-4*k^3-18*k^2+360 = 0
2*(41*k-2*k^3-9*k^2+180) = 0
41*k-2*k^3-9*k^2+180 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 9, -9, 10, -10, 12, -12, 15, -15, 18, -18, 20, -20, 30, -30, 36, -36, 45, -45, 60, -60, 90, -90, 180, -180 }
1
k = 1
41*k-2*k^3-9*k^2+180 = 210
1
-1
k = -1
41*k-2*k^3-9*k^2+180 = 132
-1
2
k = 2
41*k-2*k^3-9*k^2+180 = 210
2
-2
k = -2
41*k-2*k^3-9*k^2+180 = 78
-2
3
k = 3
41*k-2*k^3-9*k^2+180 = 168
3
-3
k = -3
41*k-2*k^3-9*k^2+180 = 30
-3
4
k = 4
41*k-2*k^3-9*k^2+180 = 72
4
-4
k = -4
41*k-2*k^3-9*k^2+180 = 0
-4
k+4
45-2*k^2-k
41*k-2*k^3-9*k^2+180
k+4
2*k^3+8*k^2
41*k-k^2+180
k^2+4*k
45*k+180
-45*k-180
0
45-2*k^2-k = 0
DELTA = (-1)^2-(-2*4*45)
DELTA = 361
DELTA > 0
k = (361^(1/2)+1)/(-2*2) or k = (1-361^(1/2))/(-2*2)
k = -5 or k = 9/2
k in { -5, 9/2, -4}
2*(k+5)*(k-9/2)*(k+4) = 0
(2*(k+5)*(k-9/2)*(k+4))/(2*(2*k+8)*(k+4)) = 0
(2*(k+5)*(k-9/2)*(k+4))/(2*(2*k+8)*(k+4)) = 0 // * 2*(2*k+8)*(k+4)
2*(k+5)*(k-9/2)*(k+4) = 0
( k+4 )
k+4 = 0 // - 4
k = -4
( k+5 )
k+5 = 0 // - 5
k = -5
( k-9/2 )
k-9/2 = 0 // + 9/2
k = 9/2
k in { -4}
k in { -5, 9/2 }
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