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Expresiones con funciones
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3*(log2(sin(x)))^2+2*log2(sin(x))-1=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 /log(sin(x))\ log(sin(x)) 3*|-----------| + 2*----------- - 1 = 0 \ log(2) / log(2)
$$\left(3 \left(\frac{\log{\left(\sin{\left(x \right)} \right)}}{\log{\left(2 \right)}}\right)^{2} + 2 \frac{\log{\left(\sin{\left(x \right)} \right)}}{\log{\left(2 \right)}}\right) - 1 = 0$$
Respuesta rápida
[src]
pi
x1 = --
6
$$x_{1} = \frac{\pi}{6}$$
5*pi
x2 = ----
6
$$x_{2} = \frac{5 \pi}{6}$$
/ /3 ___\\ / /3 ___\\ x3 = pi - re\asin\\/ 2 // - I*im\asin\\/ 2 //
$$x_{3} = - \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)}$$
/ /3 ___\\ / /3 ___\\ x4 = I*im\asin\\/ 2 // + re\asin\\/ 2 //
$$x_{4} = \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)}$$
x4 = re(asin(2^(1/3))) + i*im(asin(2^(1/3)))
Suma y producto de raíces
[src]
suma
pi 5*pi / /3 ___\\ / /3 ___\\ / /3 ___\\ / /3 ___\\ -- + ---- + pi - re\asin\\/ 2 // - I*im\asin\\/ 2 // + I*im\asin\\/ 2 // + re\asin\\/ 2 // 6 6
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)}\right) + \left(\left(\frac{\pi}{6} + \frac{5 \pi}{6}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)}\right)\right)$$
=
2*pi
$$2 \pi$$
producto
pi 5*pi / / /3 ___\\ / /3 ___\\\ / / /3 ___\\ / /3 ___\\\ --*----*\pi - re\asin\\/ 2 // - I*im\asin\\/ 2 ///*\I*im\asin\\/ 2 // + re\asin\\/ 2 /// 6 6
$$\frac{\pi}{6} \frac{5 \pi}{6} \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)}\right)$$
=
2 / / /3 ___\\ / /3 ___\\\ / / /3 ___\\ / /3 ___\\\
-5*pi *\I*im\asin\\/ 2 // + re\asin\\/ 2 ///*\-pi + I*im\asin\\/ 2 // + re\asin\\/ 2 ///
----------------------------------------------------------------------------------------
36
$$- \frac{5 \pi^{2} \left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt[3]{2} \right)}\right)}\right)}{36}$$
-5*pi^2*(i*im(asin(2^(1/3))) + re(asin(2^(1/3))))*(-pi + i*im(asin(2^(1/3))) + re(asin(2^(1/3))))/36
Respuesta numérica
[src]
x1 = -12.0427718387609
x2 = 44.5058959258554
x3 = 7.85398163397448 - 0.706232190414618*i
x4 = 39.2699081698724 + 0.706232190414618*i
x5 = -36.1283155162826 - 0.706232190414618*i
x6 = 20.4203522483337 - 0.706232190414618*i
x7 = -54.9778714378214 + 0.706232190414618*i
x8 = 34.0339204138894
x9 = 76.9690200129499 + 0.706232190414618*i
x10 = -87.4409955249159
x11 = 45.553093477052 - 0.706232190414618*i
x12 = 32.9867228626928 + 0.706232190414618*i
x13 = -5.75958653158129
x14 = 58.1194640914112 - 0.706232190414618*i
x15 = -42.4115008234622 - 0.706232190414618*i
x16 = -80.1106126665397 + 0.706232190414618*i
x17 = 95.8185759344887 - 0.706232190414618*i
x18 = -17.2787595947439 - 0.706232190414618*i
x19 = 95.8185759344887 + 0.706232190414618*i
x20 = -61.261056745001 + 0.706232190414618*i
x21 = 71.733032256967
x22 = -60.2138591938044
x23 = 83.2522053201295 - 0.706232190414618*i
x24 = -98.9601685880785 - 0.706232190414618*i
x25 = -67.5442420521806 + 0.706232190414618*i
x26 = -73.8274273593601 + 0.706232190414618*i
x27 = -42.4115008234622 + 0.706232190414618*i
x28 = -72.7802298081635
x29 = 31.9395253114962
x30 = 46.6002910282486
x31 = -23.5619449019235 - 0.706232190414618*i
x32 = 70.6858347057703 + 0.706232190414618*i
x33 = 78.0162175641465
x34 = 84.2994028713261
x35 = -18.3259571459405
x36 = 1.5707963267949 - 0.706232190414618*i
x37 = -29.845130209103 + 0.706232190414618*i
x38 = -93.7241808320955
x39 = -80.1106126665397 - 0.706232190414618*i
x40 = -3.66519142918809
x41 = 39.2699081698724 - 0.706232190414618*i
x42 = 26.7035375555132 + 0.706232190414618*i
x43 = 64.4026493985908 - 0.706232190414618*i
x44 = 83.2522053201295 + 0.706232190414618*i
x45 = -56.025068989018
x46 = 1.5707963267949 + 0.706232190414618*i
x47 = 20.4203522483337 + 0.706232190414618*i
x48 = 96.8657734856853
x49 = 27.7507351067098
x50 = 89.5353906273091 - 0.706232190414618*i
x51 = 75.9218224617533
x52 = -92.6769832808989 - 0.706232190414618*i
x53 = 14.1371669411541 - 0.706232190414618*i
x54 = -49.7418836818384
x55 = 14.1371669411541 + 0.706232190414618*i
x56 = 51.8362787842316 - 0.706232190414618*i
x57 = 58.1194640914112 + 0.706232190414618*i
x58 = -100.007366139275
x59 = -9.94837673636768
x60 = -97.9129710368819
x61 = 26.7035375555132 - 0.706232190414618*i
x62 = -68.5914396033772
x63 = -48.6946861306418 - 0.706232190414618*i
x64 = 38.2227106186758
x65 = -29.845130209103 - 0.706232190414618*i
x66 = 20.4203522483337 - 0.706232190414619*i
x67 = -43.4586983746588
x68 = 102.101761241668 + 0.706232190414618*i
x69 = -10.9955742875643 + 0.706232190414618*i
x70 = 82.2050077689329
x71 = -4.71238898038469 - 0.706232190414618*i
x72 = -24.60914245312
x73 = -23.5619449019235 + 0.706232190414618*i
x74 = -17.2787595947439 + 0.706232190414618*i
x75 = -53.9306738866248
x76 = -36.1283155162826 + 0.706232190414618*i
x77 = -91.6297857297023
x78 = -86.3937979737193 - 0.706232190414618*i
x79 = -73.8274273593601 - 0.706232190414618*i
x80 = -16.2315620435473
x81 = 40.317105721069
x82 = -47.6474885794452
x83 = 88.4881930761125
x84 = 64.4026493985908 + 0.706232190414618*i
x85 = 90.5825881785057
x85 = 90.5825881785057