π§7 = 1 2π 2π/7
π§7 = 1
π§ 7 β 1 = 0.
π§ 7 β 1 = (π§ β 1)(π§ 6 + π§ 5 + π§ 4 + π§ 3 + π§ 2 + π§ + 1) = 0
π§=1 π§6 + π§5 + π§4 + π§3 + π§2 + π§ + 1 = 0 π = 2π/7
2π
π§π = π π 7 π
ππππ
2π
π§π = π π 7 π = cos (π
π = 0, 1, β¦ ,6
2π )+ 7
π β π ππ (π
2π ) 7
π=1
2π 2π 2π π§1 = π 7 π = cos ( ) + π β π ππ ( ) 7 7
2π
cos ( 7 )
π§1
2π
π§Μ 1 = π βππ 7 = cos (
2π 2π ) β π β π ππ ( ) 7 7
π§6 + π§5 + π§4 + π§3 + π§2 + π§ + 1 = 0
2π
2π
π§1 + π§Μ 1 = π ππ 7 + π βππ 7 = π§1 +
1 π§1
2π 7
= 2 cos ( )
π§6 + π§5 + π§4 + π§3 + π§2 + π§ + 1 = 0
π§3
1 π§
π§3 + π§2 + π§ + 1 + +
π§3 +
1 π§2
+
1 π§3
=0
1 1 1 + π§2 + 2 + π§ + +1=0 3 π§ π§ π§
1 3 3 1 2 1 (π§ + ) β 3π§ β + (π§ + ) β 2 + ( π§ + ) + 1 = π§ π§ π§ π§ 1 3 1 1 2 1 (π§ + ) β 3 (π§ + ) + (π§ + ) + ( π§ + ) β 1 = 0 π§ π§ π§ π§ 1 3
1 2
1
(π§ + π§) β 2 (π§ + π§) + (π§ + π§) β 1 = 0
1
π₯ = π§+π§
π₯ 3 + π₯ 2 β 2π₯ β 1 = 0
2π
2 cos ( 7 )
2π 7
2cos( ) 2π 7
cos( )
π=
2π 9