El profesor se sorprenderá mucho al ver tu solución correcta😉
3*cos(2*x) - 5*sin(x) + 1 = 0
a*w^2 + b*w + c = 0
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (-6) * (4) = 121
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
pi x1 = -- 6
5*pi x2 = ---- 6
/ ___\ pi |4 \/ 7 | x3 = - -- + I*log|- - -----| 2 \3 3 /
/ ___\ pi |4 \/ 7 | x4 = - -- + I*log|- + -----| 2 \3 3 /
x4 = -pi/2 + i*log(sqrt(7)/3 + 4/3)
suma
/ ___\ / ___\ pi 5*pi pi |4 \/ 7 | pi |4 \/ 7 | -- + ---- + - -- + I*log|- - -----| + - -- + I*log|- + -----| 6 6 2 \3 3 / 2 \3 3 /
=
/ ___\ / ___\ |4 \/ 7 | |4 \/ 7 | I*log|- - -----| + I*log|- + -----| \3 3 / \3 3 /
producto
/ / ___\\ / / ___\\ pi 5*pi | pi |4 \/ 7 || | pi |4 \/ 7 || --*----*|- -- + I*log|- - -----||*|- -- + I*log|- + -----|| 6 6 \ 2 \3 3 // \ 2 \3 3 //
=
/ / 2\\ / / 2\\ | |/ ___\ || | |/ ___\ || 2 | |\4 + \/ 7 / || | |\4 - \/ 7 / || 5*pi *|pi - I*log|------------||*|pi - I*log|------------|| \ \ 9 // \ \ 9 // ----------------------------------------------------------- 144
5*pi^2*(pi - i*log((4 + sqrt(7))^2/9))*(pi - i*log((4 - sqrt(7))^2/9))/144
x1 = -3.66519142918809
x2 = 90.5825881785057
x3 = -49.7418836818384
x4 = -81.1578102177363
x5 = 38.2227106186758
x6 = 88.4881930761125
x7 = 31.9395253114962
x8 = 44.5058959258554
x9 = 27.7507351067098
x10 = -5.75958653158129
x11 = -93.7241808320955
x12 = -35.081117965086
x13 = -72.7802298081635
x14 = -91.6297857297023
x15 = 75.9218224617533
x16 = -68.5914396033772
x17 = 96.8657734856853
x18 = -9.94837673636768
x19 = 34.0339204138894
x20 = -56.025068989018
x21 = 65.4498469497874
x22 = -24.60914245312
x23 = -66.497044500984
x24 = 94.7713783832921
x25 = -16.2315620435473
x26 = 69.6386371545737
x27 = -43.4586983746588
x28 = 8.90117918517108
x29 = 52.8834763354282
x30 = 63.3554518473942
x31 = 19.3731546971371
x32 = -18.3259571459405
x33 = 115.715329407224
x34 = 2.61799387799149
x35 = 21.4675497995303
x36 = -62.3082542961976
x37 = -41.3643032722656
x38 = 25.6563400043166
x39 = -1203.75358510049
x40 = -85.3466004225227
x41 = 6.80678408277789
x42 = -97.9129710368819
x43 = 50.789081233035
x44 = -87.4409955249159
x45 = 84.2994028713261
x46 = -53.9306738866248
x47 = -22.5147473507269
x48 = -60.2138591938044
x49 = 46.6002910282486
x50 = -100.007366139275
x51 = 40.317105721069
x52 = -12.0427718387609
x53 = -110.479341651241
x54 = 82.2050077689329
x55 = -47.6474885794452
x56 = 78.0162175641465
x57 = 71.733032256967
x58 = -37.1755130674792
x59 = 0.523598775598299
x60 = -79.0634151153431
x60 = -79.0634151153431