Найду корень уравнения: 4^cos(x)=2
pi x1 = -- 3
5*pi x2 = ---- 3
/ /1 pi*I \\ / /1 pi*I \\ x3 = - re|acos|- + ------|| + 2*pi - I*im|acos|- + ------|| \ \2 log(2)// \ \2 log(2)//
/ /1 pi*I \\ / /1 pi*I \\ x4 = I*im|acos|- + ------|| + re|acos|- + ------|| \ \2 log(2)// \ \2 log(2)//
сумма
pi 5*pi / /1 pi*I \\ / /1 pi*I \\ / /1 pi*I \\ / /1 pi*I \\ -- + ---- + - re|acos|- + ------|| + 2*pi - I*im|acos|- + ------|| + I*im|acos|- + ------|| + re|acos|- + ------|| 3 3 \ \2 log(2)// \ \2 log(2)// \ \2 log(2)// \ \2 log(2)//
=
4*pi
произведение
pi 5*pi / / /1 pi*I \\ / /1 pi*I \\\ / / /1 pi*I \\ / /1 pi*I \\\ --*----*|- re|acos|- + ------|| + 2*pi - I*im|acos|- + ------|||*|I*im|acos|- + ------|| + re|acos|- + ------||| 3 3 \ \ \2 log(2)// \ \2 log(2)/// \ \ \2 log(2)// \ \2 log(2)///
=
2 / / /2*pi*I + log(2)\\ / /2*pi*I + log(2)\\\ / / /2*pi*I + log(2)\\ / /2*pi*I + log(2)\\\ -5*pi *|I*im|acos|---------------|| + re|acos|---------------|||*|-2*pi + I*im|acos|---------------|| + re|acos|---------------||| \ \ \ 2*log(2) // \ \ 2*log(2) /// \ \ \ 2*log(2) // \ \ 2*log(2) /// ---------------------------------------------------------------------------------------------------------------------------------- 9
x1 = 55.5014702134197
x2 = -93.2005820564972
x3 = 26.1799387799149
x4 = 42.9350995990605
x5 = -7.33038285837618
x6 = -17.8023583703422
x7 = 5.23598775598299
x8 = 70.162235930172
x9 = 11.5191730631626
x10 = -49.2182849062401
x11 = 74.3510261349584
x12 = -76.4454212373516
x13 = -19.8967534727354
x14 = 89.0117918517108
x15 = 32.4631240870945
x16 = 132.994089001968
x17 = -74.3510261349584
x18 = 93.2005820564972
x19 = -143.466064513934
x20 = 86.9173967493176
x21 = 76.4454212373516
x22 = -82.7286065445312
x23 = 36.6519142918809
x24 = 82.7286065445312
x25 = 38.7463093942741
x26 = -42.9350995990605
x27 = -24.0855436775217
x28 = -36.6519142918809
x29 = 30.3687289847013
x30 = -68.0678408277789
x31 = 24.0855436775217
x32 = -99.4837673636768
x33 = 61.7846555205993
x34 = -45.0294947014537
x35 = -57.5958653158129
x36 = -63.8790506229925
x37 = -26.1799387799149
x38 = -95.2949771588904
x39 = -86.9173967493176
x40 = 99.4837673636768
x41 = 45.0294947014537
x42 = -13.6135681655558
x43 = 63.8790506229925
x44 = -32.4631240870945
x45 = 68.0678408277789
x46 = 13.6135681655558
x47 = -101.57816246607
x48 = 51.3126800086333
x49 = -70.162235930172
x50 = -89.0117918517108
x51 = -5.23598775598299
x52 = -114.144533080429
x53 = 19.8967534727354
x54 = -38.7463093942741
x55 = -1.0471975511966
x56 = 1.0471975511966
x57 = -51.3126800086333
x58 = -80.634211442138
x59 = 7.33038285837618
x60 = 49.2182849062401
x61 = 271.224165759919
x62 = -61.7846555205993
x63 = -55.5014702134197
x64 = -30.3687289847013
x65 = -11.5191730631626
x66 = 80.634211442138
x67 = 17.8023583703422
x68 = 95.2949771588904
x69 = 57.5958653158129