El profesor se sorprenderá mucho al ver tu solución correcta😉
2 sin(x) + cos (x) = 1/4
a*w^2 + b*w + c = 0
D = b^2 - 4 * a * c =
(1)^2 - 4 * (-1) * (3/4) = 4
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
suma
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ 5*pi pi | |2 I*\/ 5 || | |2 I*\/ 5 || | |2 I*\/ 5 || | |2 I*\/ 5 || - ---- - -- + 2*re|atan|- - -------|| + 2*I*im|atan|- - -------|| + 2*re|atan|- + -------|| + 2*I*im|atan|- + -------|| 6 6 \ \3 3 // \ \3 3 // \ \3 3 // \ \3 3 //
=
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ | |2 I*\/ 5 || | |2 I*\/ 5 || | |2 I*\/ 5 || | |2 I*\/ 5 || -pi + 2*re|atan|- - -------|| + 2*re|atan|- + -------|| + 2*I*im|atan|- - -------|| + 2*I*im|atan|- + -------|| \ \3 3 // \ \3 3 // \ \3 3 // \ \3 3 //
producto
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ -5*pi -pi | | |2 I*\/ 5 || | |2 I*\/ 5 ||| | | |2 I*\/ 5 || | |2 I*\/ 5 ||| -----*----*|2*re|atan|- - -------|| + 2*I*im|atan|- - -------|||*|2*re|atan|- + -------|| + 2*I*im|atan|- + -------||| 6 6 \ \ \3 3 // \ \3 3 /// \ \ \3 3 // \ \3 3 ///
=
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ 2 | | |2 I*\/ 5 || | |2 I*\/ 5 ||| | | |2 I*\/ 5 || | |2 I*\/ 5 ||| 5*pi *|I*im|atan|- - -------|| + re|atan|- - -------|||*|I*im|atan|- + -------|| + re|atan|- + -------||| \ \ \3 3 // \ \3 3 /// \ \ \3 3 // \ \3 3 /// --------------------------------------------------------------------------------------------------------- 9
5*pi^2*(i*im(atan(2/3 - i*sqrt(5)/3)) + re(atan(2/3 - i*sqrt(5)/3)))*(i*im(atan(2/3 + i*sqrt(5)/3)) + re(atan(2/3 + i*sqrt(5)/3)))/9
-5*pi x1 = ----- 6
-pi x2 = ---- 6
/ / ___\\ / / ___\\ | |2 I*\/ 5 || | |2 I*\/ 5 || x3 = 2*re|atan|- - -------|| + 2*I*im|atan|- - -------|| \ \3 3 // \ \3 3 //
/ / ___\\ / / ___\\ | |2 I*\/ 5 || | |2 I*\/ 5 || x4 = 2*re|atan|- + -------|| + 2*I*im|atan|- + -------|| \ \3 3 // \ \3 3 //
x4 = 2*re(atan(2/3 + sqrt(5)*i/3)) + 2*i*im(atan(2/3 + sqrt(5)*i/3))
x1 = -15.1843644923507
x2 = 18.3259571459405
x3 = 66.497044500984
x4 = 93.7241808320955
x5 = -57.0722665402146
x6 = -25.6563400043166
x7 = 56.025068989018
x8 = 47.6474885794452
x9 = -78.0162175641465
x10 = 5.75958653158129
x11 = -82.2050077689329
x12 = 28.7979326579064
x13 = 81.1578102177363
x14 = 97.9129710368819
x15 = -0.523598775598299
x16 = 68.5914396033772
x17 = -90.5825881785057
x18 = 43.4586983746588
x19 = 100.007366139275
x20 = -46.6002910282486
x21 = 30.8923277602996
x22 = 37.1755130674792
x23 = -63.3554518473942
x24 = -27.7507351067098
x25 = -34.0339204138894
x26 = -44.5058959258554
x27 = 79.0634151153431
x28 = 91.6297857297023
x29 = -65.4498469497874
x30 = 72.7802298081635
x31 = 60.2138591938044
x32 = -71.733032256967
x33 = -31.9395253114962
x34 = 53.9306738866248
x35 = 3.66519142918809
x36 = 22.5147473507269
x37 = -84.2994028713261
x38 = -88.4881930761125
x39 = -40.317105721069
x40 = -69.6386371545737
x41 = -50.789081233035
x42 = -6.80678408277789
x43 = -19.3731546971371
x44 = -103.148958792865
x45 = 87.4409955249159
x46 = 16.2315620435473
x47 = -38.2227106186758
x48 = 62.3082542961976
x49 = -94.7713783832921
x50 = 49.7418836818384
x51 = 85.3466004225227
x52 = 74.8746249105567
x53 = 12.0427718387609
x54 = -21.4675497995303
x55 = -59.1666616426078
x56 = -13.0899693899575
x57 = 41.3643032722656
x58 = 24.60914245312
x59 = 35.081117965086
x60 = -75.9218224617533
x61 = 9.94837673636768
x62 = -2.61799387799149
x62 = -2.61799387799149