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D( k )
4*k^2+8*k+3 = 0
4*k^2-1 = 0
4*k^2+8*k+3 = 0
4*k^2+8*k+3 = 0
4*k^2+8*k+3 = 0
DELTA = 8^2-(3*4*4)
DELTA = 16
DELTA > 0
k = (16^(1/2)-8)/(2*4) or k = (-16^(1/2)-8)/(2*4)
k = -1/2 or k = -3/2
4*k^2-1 = 0
4*k^2-1 = 0
4*k^2 = 1 // : 4
k^2 = 1/4
k^2 = 1/4 // ^ 1/2
abs(k) = 1/2
k = 1/2 or k = -1/2
k in (-oo:-3/2) U (-3/2:-1/2) U (-1/2:1/2) U (1/2:+oo)
k/(4*k^2-1)+2/(4*k^2+8*k+3) = 0
4*k^2+8*k+3 = 0
4*k^2+8*k+3 = 0
4*k^2+8*k+3 = 0
DELTA = 8^2-(3*4*4)
DELTA = 16
DELTA > 0
k = (16^(1/2)-8)/(2*4) or k = (-16^(1/2)-8)/(2*4)
k = -1/2 or k = -3/2
(k+3/2)*(k+1/2) = 0
k/(4*k^2-1)+2/((k+3/2)*(k+1/2)) = 0
(k*(k+3/2)*(k+1/2))/((4*k^2-1)*(k+3/2)*(k+1/2))+(2*(4*k^2-1))/((4*k^2-1)*(k+3/2)*(k+1/2)) = 0
k*(k+3/2)*(k+1/2)+2*(4*k^2-1) = 0
k^3+10*k^2+3/4*k-2 = 0
k^3+10*k^2+3/4*k-2 = 0
k^3+10*k^2+(3/4)*k-2 = 0
k^3+10*k^2+(3/4)*k-2 = 0 // * 0
{ 1, -1, 2, -2, 4, -4, 8, -8 }
1
k = 1
4*k^3+40*k^2+3*k-8 = 39
1
-1
k = -1
4*k^3+40*k^2+3*k-8 = 25
-1
2
k = 2
4*k^3+40*k^2+3*k-8 = 190
2
-2
k = -2
4*k^3+40*k^2+3*k-8 = 114
-2
4
k = 4
4*k^3+40*k^2+3*k-8 = 900
4
-4
k = -4
4*k^3+40*k^2+3*k-8 = 364
-4
8
k = 8
4*k^3+40*k^2+3*k-8 = 4624
8
-8
k = -8
4*k^3+40*k^2+3*k-8 = 480
-8
{ 1/2, -1/2, 1/4, -1/4, -1/2, 1/2, -1/4, 1/4, 2/2, -2/2, 2/4, -2/4, -2/2, 2/2, -2/4, 2/4, 4/2, -4/2, 4/4, -4/4, -4/2, 4/2, -4/4, 4/4, 8/2, -8/2, 8/4, -8/4, -8/2, 8/2, -8/4, 8/4 }
1/2
k
1/2
4*k^3+40*k^2+3*k-8 = 4
1/2
-1/2
k
-1/2
4*k^3+40*k^2+3*k-8 = 0
-1/2
k+1/2
4*k^2+38*k-16
4*k^3+40*k^2+3*k-8
k+1/2
-4*k^3-2*k^2
38*k^2+3*k-8
-38*k^2-19*k
-16*k-8
16*k+8
0
4*k^2+38*k-16 = 0
DELTA = 38^2-(-16*4*4)
DELTA = 1700
DELTA > 0
k = (1700^(1/2)-38)/(2*4) or k = (-1700^(1/2)-38)/(2*4)
k = (10*17^(1/2)-38)/8 or k = (-10*17^(1/2)-38)/8
k in { (-10*17^(1/2)-38)/8, (10*17^(1/2)-38)/8, -1/2}
(k-((-10*17^(1/2)-38)/8))*(k-((10*17^(1/2)-38)/8))*(k+1/2) = 0
((k-((-10*17^(1/2)-38)/8))*(k-((10*17^(1/2)-38)/8))*(k+1/2))/((4*k^2-1)*(k+3/2)*(k+1/2)) = 0
((k-((-10*17^(1/2)-38)/8))*(k-((10*17^(1/2)-38)/8))*(k+1/2))/((4*k^2-1)*(k+3/2)*(k+1/2)) = 0 // * (4*k^2-1)*(k+3/2)*(k+1/2)
(k-((-10*17^(1/2)-38)/8))*(k-((10*17^(1/2)-38)/8))*(k+1/2) = 0
( k+1/2 )
k+1/2 = 0 // - 1/2
k = -1/2
( k-((-10*17^(1/2)-38)/8) )
k-((-10*17^(1/2)-38)/8) = 0 // + (-10*17^(1/2)-38)/8
k = (-10*17^(1/2)-38)/8
( k-((10*17^(1/2)-38)/8) )
k-((10*17^(1/2)-38)/8) = 0 // + (10*17^(1/2)-38)/8
k = (10*17^(1/2)-38)/8
k in { -1/2}
k in { (-10*17^(1/2)-38)/8, (10*17^(1/2)-38)/8 }
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