Sr Examen
2*cos^3x-cos^2x+2cosx-1=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 2*cos (x) - cos (x) + 2*cos(x) - 1 = 0
$$\left(\left(2 \cos^{3}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) + 2 \cos{\left(x \right)}\right) - 1 = 0$$
Respuesta rápida
[src]
pi
x1 = --
3
$$x_{1} = \frac{\pi}{3}$$
5*pi
x2 = ----
3
$$x_{2} = \frac{5 \pi}{3}$$
pi / ___\
x3 = -- - I*log\1 + \/ 2 /
2
$$x_{3} = \frac{\pi}{2} - i \log{\left(1 + \sqrt{2} \right)}$$
pi / ___\
x4 = -- + I*log\1 + \/ 2 /
2
$$x_{4} = \frac{\pi}{2} + i \log{\left(1 + \sqrt{2} \right)}$$
3*pi / ___\
x5 = ---- - I*log\1 + \/ 2 /
2
$$x_{5} = \frac{3 \pi}{2} - i \log{\left(1 + \sqrt{2} \right)}$$
3*pi / ___\
x6 = ---- + I*log\1 + \/ 2 /
2
$$x_{6} = \frac{3 \pi}{2} + i \log{\left(1 + \sqrt{2} \right)}$$
x6 = 3*pi/2 + i*log(1 + sqrt(2))
Suma y producto de raíces
[src]
suma
pi 5*pi pi / ___\ pi / ___\ 3*pi / ___\ 3*pi / ___\ -- + ---- + -- - I*log\1 + \/ 2 / + -- + I*log\1 + \/ 2 / + ---- - I*log\1 + \/ 2 / + ---- + I*log\1 + \/ 2 / 3 3 2 2 2 2
$$\left(\left(\frac{3 \pi}{2} - i \log{\left(1 + \sqrt{2} \right)}\right) + \left(\left(\left(\frac{\pi}{3} + \frac{5 \pi}{3}\right) + \left(\frac{\pi}{2} - i \log{\left(1 + \sqrt{2} \right)}\right)\right) + \left(\frac{\pi}{2} + i \log{\left(1 + \sqrt{2} \right)}\right)\right)\right) + \left(\frac{3 \pi}{2} + i \log{\left(1 + \sqrt{2} \right)}\right)$$
=
6*pi
$$6 \pi$$
producto
pi 5*pi /pi / ___\\ /pi / ___\\ /3*pi / ___\\ /3*pi / ___\\ --*----*|-- - I*log\1 + \/ 2 /|*|-- + I*log\1 + \/ 2 /|*|---- - I*log\1 + \/ 2 /|*|---- + I*log\1 + \/ 2 /| 3 3 \2 / \2 / \ 2 / \ 2 /
$$\frac{\pi}{3} \frac{5 \pi}{3} \left(\frac{\pi}{2} - i \log{\left(1 + \sqrt{2} \right)}\right) \left(\frac{\pi}{2} + i \log{\left(1 + \sqrt{2} \right)}\right) \left(\frac{3 \pi}{2} - i \log{\left(1 + \sqrt{2} \right)}\right) \left(\frac{3 \pi}{2} + i \log{\left(1 + \sqrt{2} \right)}\right)$$
=
2 / 4 4/ ___\ 2 2/ ___\\
5*pi *\9*pi + 16*log \1 + \/ 2 / + 40*pi *log \1 + \/ 2 //
-----------------------------------------------------------
144
$$\frac{5 \pi^{2} \left(16 \log{\left(1 + \sqrt{2} \right)}^{4} + 40 \pi^{2} \log{\left(1 + \sqrt{2} \right)}^{2} + 9 \pi^{4}\right)}{144}$$
5*pi^2*(9*pi^4 + 16*log(1 + sqrt(2))^4 + 40*pi^2*log(1 + sqrt(2))^2)/144
Respuesta numérica
[src]
x1 = -55.5014702134197
x2 = 11.5191730631626
x3 = 99.4837673636768
x4 = -11.5191730631626
x5 = -42.9350995990605
x6 = -30.3687289847013
x7 = -1.0471975511966
x8 = -89.0117918517108
x9 = -38.7463093942741
x10 = 30.3687289847013
x11 = -49.2182849062401
x12 = -32.4631240870945
x13 = 36.6519142918809
x14 = 38.7463093942741
x15 = 93.2005820564972
x16 = -74.3510261349584
x17 = 74.3510261349584
x18 = 55.5014702134197
x19 = 1.0471975511966
x20 = 51.3126800086333
x21 = 17.8023583703422
x22 = -51.3126800086333
x23 = 95.2949771588904
x24 = -564.439480094966
x25 = -57.5958653158129
x26 = -99.4837673636768
x27 = -82.7286065445312
x28 = 26.1799387799149
x29 = 76.4454212373516
x30 = 57.5958653158129
x31 = 82.7286065445312
x32 = 86.9173967493176
x33 = -61.7846555205993
x34 = 24.0855436775217
x35 = -17.8023583703422
x36 = -26.1799387799149
x37 = 5.23598775598299
x38 = 49.2182849062401
x39 = 45.0294947014537
x40 = 32.4631240870945
x41 = 70.162235930172
x42 = -70.162235930172
x43 = -80.634211442138
x44 = -5.23598775598299
x45 = 89.0117918517108
x46 = -68.0678408277789
x47 = 80.634211442138
x48 = -24.0855436775217
x49 = -95.2949771588904
x50 = -13.6135681655558
x51 = 61.7846555205993
x52 = -93.2005820564972
x53 = 63.8790506229925
x54 = -76.4454212373516
x55 = -63.8790506229925
x56 = 42.9350995990605
x57 = -36.6519142918809
x58 = 68.0678408277789
x59 = -7.33038285837618
x60 = -19.8967534727354
x61 = -45.0294947014537
x62 = 19.8967534727354
x63 = 7.33038285837618
x64 = -86.9173967493176
x65 = 13.6135681655558
x65 = 13.6135681655558