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Ecuación -x+7=0
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Ecuación x+(x/4)=-5
- Ecuación z^4-81=0
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Ecuación z^3=8
- Expresar {x} en función de y en la ecuación:
- -18*x-8*y=-18
- -13*x+12*y=-19
- -1*x+11*y=-9
- 16*x-11*y=13
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Expresiones idénticas
- 2cos4a-2cos2a=4cos^2a- uno
- 2 coseno de 4a menos 2 coseno de 2a es igual a 4 coseno de al cuadrado a menos 1
- 2 coseno de 4a menos 2 coseno de 2a es igual a 4 coseno de al cuadrado a menos uno
- 2cos4a-2cos2a=4cos2a-1
- 2cos4a-2cos2a=4cos²a-1
- 2cos4a-2cos2a=4cos en el grado 2a-1
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Expresiones semejantes
- 2cos4a-2cos2a=4cos^2a+1
- 2cos4a+2cos2a=4cos^2a-1
2cos4a-2cos2a=4cos^2a-1 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2*cos(4*a) - 2*cos(2*a) = 4*cos (a) - 1
$$- 2 \cos{\left(2 a \right)} + 2 \cos{\left(4 a \right)} = 4 \cos^{2}{\left(a \right)} - 1$$
Respuesta rápida
[src]
-2*pi
a1 = -----
3
$$a_{1} = - \frac{2 \pi}{3}$$
-pi
a2 = ----
3
$$a_{2} = - \frac{\pi}{3}$$
pi
a3 = --
3
$$a_{3} = \frac{\pi}{3}$$
2*pi
a4 = ----
3
$$a_{4} = \frac{2 \pi}{3}$$
/ ___\
| 1 \/ 5 |
a5 = I*log|- - + -----|
\ 2 2 /
$$a_{5} = i \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
/ ___\
|1 \/ 5 |
a6 = I*log|- + -----|
\2 2 /
$$a_{6} = i \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
/ ___\
| 1 \/ 5 |
a7 = pi + I*log|- - + -----|
\ 2 2 /
$$a_{7} = \pi + i \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
/ ___\
|1 \/ 5 |
a8 = pi + I*log|- + -----|
\2 2 /
$$a_{8} = \pi + i \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
a8 = pi + i*log(1/2 + sqrt(5)/2)
Suma y producto de raíces
[src]
suma
/ ___\ / ___\ / ___\ / ___\ 2*pi pi pi 2*pi | 1 \/ 5 | |1 \/ 5 | | 1 \/ 5 | |1 \/ 5 | - ---- - -- + -- + ---- + I*log|- - + -----| + I*log|- + -----| + pi + I*log|- - + -----| + pi + I*log|- + -----| 3 3 3 3 \ 2 2 / \2 2 / \ 2 2 / \2 2 /
$$\left(\left(\pi + i \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}\right) + \left(\left(\left(\left(\left(- \frac{2 \pi}{3} - \frac{\pi}{3}\right) + \frac{\pi}{3}\right) + \frac{2 \pi}{3}\right) + i \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}\right) + i \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}\right)\right) + \left(\pi + i \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}\right)$$
=
/ ___\ / ___\
|1 \/ 5 | | 1 \/ 5 |
2*pi + 2*I*log|- + -----| + 2*I*log|- - + -----|
\2 2 / \ 2 2 /
$$2 \pi + 2 i \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + 2 i \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
producto
/ ___\ / ___\ / / ___\\ / / ___\\ -2*pi -pi pi 2*pi | 1 \/ 5 | |1 \/ 5 | | | 1 \/ 5 || | |1 \/ 5 || -----*----*--*----*I*log|- - + -----|*I*log|- + -----|*|pi + I*log|- - + -----||*|pi + I*log|- + -----|| 3 3 3 3 \ 2 2 / \2 2 / \ \ 2 2 // \ \2 2 //
$$i \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} i \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)} \frac{2 \pi}{3} \frac{\pi}{3} \cdot - \frac{2 \pi}{3} \left(- \frac{\pi}{3}\right) \left(\pi + i \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}\right) \left(\pi + i \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}\right)$$
=
/ / 4\\
| | 4*pi ||
| | -----||
| | 81 ||
| |/ ___\ ||
| || 1 \/ 5 | ||
| log||- - + -----| ||
| \\ 2 2 / /|
/ / ___\\ / / ___\\ |/ ___\ |
| |1 \/ 5 || | | 1 \/ 5 || ||1 \/ 5 | |
-|pi + I*log|- + -----||*|pi + I*log|- - + -----||*log||- + -----| |
\ \2 2 // \ \ 2 2 // \\2 2 / /
$$- \left(\pi + i \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}\right) \left(\pi + i \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}\right) \log{\left(\left(\frac{1}{2} + \frac{\sqrt{5}}{2}\right)^{\log{\left(\left(- \frac{1}{2} + \frac{\sqrt{5}}{2}\right)^{\frac{4 \pi^{4}}{81}} \right)}} \right)}$$
-(pi + i*log(1/2 + sqrt(5)/2))*(pi + i*log(-1/2 + sqrt(5)/2))*log((1/2 + sqrt(5)/2)^log((-1/2 + sqrt(5)/2)^(4*pi^4/81)))
Respuesta numérica
[src]
a1 = -24.0855436775217
a2 = -46.0766922526503
a3 = -51.3126800086333
a4 = 32.4631240870945
a5 = -54.4542726622231
a6 = 101.57816246607
a7 = -4.18879020478639
a8 = -57.5958653158129
a9 = 90.0589894029074
a10 = 76.4454212373516
a11 = 95.2949771588904
a12 = -79.5870138909414
a13 = 8.37758040957278
a14 = -95.2949771588904
a15 = 4.18879020478639
a16 = 98.4365698124802
a17 = -14.6607657167524
a18 = 51.3126800086333
a19 = 42.9350995990605
a20 = -30.3687289847013
a21 = 46.0766922526503
a22 = -7.33038285837618
a23 = -41.8879020478639
a24 = -92.1533845053006
a25 = -23.0383461263252
a26 = -29.3215314335047
a27 = 39.7935069454707
a28 = -39.7935069454707
a29 = 7.33038285837618
a30 = -99.4837673636768
a31 = 79.5870138909414
a32 = -33.5103216382911
a33 = -13.6135681655558
a34 = 83.7758040957278
a35 = 19.8967534727354
a36 = -73.3038285837618
a37 = -1.0471975511966
a38 = -48.1710873550435
a39 = 41.8879020478639
a40 = 63.8790506229925
a41 = 68.0678408277789
a42 = 74.3510261349584
a43 = 64.9262481741891
a44 = -90.0589894029074
a45 = 57.5958653158129
a46 = -80.634211442138
a47 = -85.870199198121
a48 = 20.943951023932
a49 = -61.7846555205993
a50 = -77.4926187885482
a51 = -11.5191730631626
a52 = -2.0943951023932
a53 = -35.6047167406843
a54 = 26.1799387799149
a55 = 52.3598775598299
a56 = 54.4542726622231
a57 = 86.9173967493176
a58 = 96.342174710087
a59 = -19.8967534727354
a60 = -68.0678408277789
a61 = 85.870199198121
a62 = -70.162235930172
a63 = 36.6519142918809
a64 = -83.7758040957278
a65 = -58.6430628670095
a66 = 70.162235930172
a67 = -17.8023583703422
a68 = 2.0943951023932
a69 = 29.3215314335047
a70 = 48.1710873550435
a71 = -55.5014702134197
a72 = 24.0855436775217
a73 = -36.6519142918809
a74 = 14.6607657167524
a75 = -63.8790506229925
a76 = 73.3038285837618
a77 = 10.471975511966
a78 = 92.1533845053006
a79 = 61.7846555205993
a80 = 17.8023583703422
a81 = -26.1799387799149
a82 = 30.3687289847013
a82 = 30.3687289847013