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Ecuación 6*x^2+x-7=0
- Ecuación z^5+32=0
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Ecuación 2-5(3+2x)=17
-
Ecuación (6*x+8)/2+5=5*x/3
- Expresar {x} en función de y en la ecuación:
- -9*x-12*y=-19
- -8*x+3*y=-4
- 10*x+3*y=2
- 16*x-17*y=-15
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Expresiones idénticas
- sqrt2*cos5x+sin3x-sin7x= cero
- raíz cuadrada de 2 multiplicar por coseno de 5x más seno de 3x menos seno de 7x es igual a 0
- raíz cuadrada de 2 multiplicar por coseno de 5x más seno de 3x menos seno de 7x es igual a cero
- √2*cos5x+sin3x-sin7x=0
- sqrt2cos5x+sin3x-sin7x=0
- sqrt2*cos5x+sin3x-sin7x=O
-
Expresiones semejantes
- sqrt2*cos5x-sin3x-sin7x=0
- sqrt2*cos5x+sin3x+sin7x=0
sqrt2*cos5x+sin3x-sin7x=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___ \/ 2 *cos(5*x) + sin(3*x) - sin(7*x) = 0
$$\left(\sin{\left(3 x \right)} + \sqrt{2} \cos{\left(5 x \right)}\right) - \sin{\left(7 x \right)} = 0$$
Suma y producto de raíces
[src]
suma
/ ___________\ / ___________\
| / ___ | | / ___ |
| / 1 \/ 2 | | / 1 \/ 2 |
| / - + ----- | | / - - ----- |
9*pi 7*pi pi 3*pi pi pi pi 3*pi 3*pi pi 7*pi 9*pi / /4 ___\ log(2)\ |\/ 2 4 | / /4 ___\ log(2)\ |\/ 2 4 |
- ---- - ---- - -- - ---- - -- + -- + -- + ---- + ---- + -- + ---- + ---- + -pi + I*|- log\\/ 2 / + ------| + atan|----------------| + -pi + I*|- log\\/ 2 / + ------| + atan|----------------|
10 10 2 10 10 10 8 10 8 2 10 10 \ 4 / | ___________| \ 4 / | ___________|
| / ___ | | / ___ |
| / 1 \/ 2 | | / 1 \/ 2 |
| / - - ----- | | / - + ----- |
\\/ 2 4 / \\/ 2 4 /
$$\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(- \frac{9 \pi}{10} - \frac{7 \pi}{10}\right) - \frac{\pi}{2}\right) - \frac{3 \pi}{10}\right) - \frac{\pi}{10}\right) + \frac{\pi}{10}\right) + \frac{\pi}{8}\right) + \frac{3 \pi}{10}\right) + \frac{3 \pi}{8}\right) + \frac{\pi}{2}\right) + \frac{7 \pi}{10}\right) + \frac{9 \pi}{10}\right) + \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}} \right)} + i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)\right)\right) + \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}} \right)} + i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)\right)$$
=
/ ___________\ / ___________\
| / ___ | | / ___ |
| / 1 \/ 2 | | / 1 \/ 2 |
| / - - ----- | | / - + ----- |
3*pi / /4 ___\ log(2)\ |\/ 2 4 | |\/ 2 4 |
- ---- + 2*I*|- log\\/ 2 / + ------| + atan|----------------| + atan|----------------|
2 \ 4 / | ___________| | ___________|
| / ___ | | / ___ |
| / 1 \/ 2 | | / 1 \/ 2 |
| / - + ----- | | / - - ----- |
\\/ 2 4 / \\/ 2 4 /
$$- \frac{3 \pi}{2} + \operatorname{atan}{\left(\frac{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}} \right)} + \operatorname{atan}{\left(\frac{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}} \right)} + 2 i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)$$
producto
/ / ___________\\ / / ___________\\
| | / ___ || | | / ___ ||
| | / 1 \/ 2 || | | / 1 \/ 2 ||
| | / - + ----- || | | / - - ----- ||
-9*pi -7*pi -pi -3*pi -pi pi pi 3*pi 3*pi pi 7*pi 9*pi | / /4 ___\ log(2)\ |\/ 2 4 || | / /4 ___\ log(2)\ |\/ 2 4 ||
-----*-----*----*-----*----*--*--*----*----*--*----*----*|-pi + I*|- log\\/ 2 / + ------| + atan|----------------||*|-pi + I*|- log\\/ 2 / + ------| + atan|----------------||
10 10 2 10 10 10 8 10 8 2 10 10 | \ 4 / | ___________|| | \ 4 / | ___________||
| | / ___ || | | / ___ ||
| | / 1 \/ 2 || | | / 1 \/ 2 ||
| | / - - ----- || | | / - + ----- ||
\ \\/ 2 4 // \ \\/ 2 4 //
$$\frac{9 \pi}{10} \frac{7 \pi}{10} \frac{\pi}{2} \frac{3 \pi}{8} \frac{3 \pi}{10} \frac{\pi}{8} \frac{\pi}{10} \cdot - \frac{\pi}{10} \cdot - \frac{3 \pi}{10} \cdot - \frac{\pi}{2} \cdot - \frac{9 \pi}{10} \left(- \frac{7 \pi}{10}\right) \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}} \right)} + i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)\right) \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}} \right)} + i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)\right)$$
=
/ / ___________\\ / / ___________\\
| | / ___ || | | / ___ ||
12 | |\/ 2 + \/ 2 || | |\/ 2 - \/ 2 ||
-107163*pi *|pi - atan|--------------||*|pi - atan|--------------||
| | ___________|| | | ___________||
| | / ___ || | | / ___ ||
\ \\/ 2 - \/ 2 // \ \\/ 2 + \/ 2 //
--------------------------------------------------------------------
25600000000
$$- \frac{107163 \pi^{12} \left(\pi - \operatorname{atan}{\left(\frac{\sqrt{\sqrt{2} + 2}}{\sqrt{2 - \sqrt{2}}} \right)}\right) \left(\pi - \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}\right)}{25600000000}$$
-107163*pi^12*(pi - atan(sqrt(2 + sqrt(2))/sqrt(2 - sqrt(2))))*(pi - atan(sqrt(2 - sqrt(2))/sqrt(2 + sqrt(2))))/25600000000
Respuesta rápida
[src]
-9*pi
x1 = -----
10
$$x_{1} = - \frac{9 \pi}{10}$$
-7*pi
x2 = -----
10
$$x_{2} = - \frac{7 \pi}{10}$$
-pi
x3 = ----
2
$$x_{3} = - \frac{\pi}{2}$$
-3*pi
x4 = -----
10
$$x_{4} = - \frac{3 \pi}{10}$$
-pi
x5 = ----
10
$$x_{5} = - \frac{\pi}{10}$$
pi
x6 = --
10
$$x_{6} = \frac{\pi}{10}$$
pi
x7 = --
8
$$x_{7} = \frac{\pi}{8}$$
3*pi
x8 = ----
10
$$x_{8} = \frac{3 \pi}{10}$$
3*pi
x9 = ----
8
$$x_{9} = \frac{3 \pi}{8}$$
pi
x10 = --
2
$$x_{10} = \frac{\pi}{2}$$
7*pi
x11 = ----
10
$$x_{11} = \frac{7 \pi}{10}$$
9*pi
x12 = ----
10
$$x_{12} = \frac{9 \pi}{10}$$
/ ___________\
| / ___ |
| / 1 \/ 2 |
| / - + ----- |
/ /4 ___\ log(2)\ |\/ 2 4 |
x13 = -pi + I*|- log\\/ 2 / + ------| + atan|----------------|
\ 4 / | ___________|
| / ___ |
| / 1 \/ 2 |
| / - - ----- |
\\/ 2 4 /
$$x_{13} = - \pi + \operatorname{atan}{\left(\frac{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}} \right)} + i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)$$
/ ___________\
| / ___ |
| / 1 \/ 2 |
| / - - ----- |
/ /4 ___\ log(2)\ |\/ 2 4 |
x14 = -pi + I*|- log\\/ 2 / + ------| + atan|----------------|
\ 4 / | ___________|
| / ___ |
| / 1 \/ 2 |
| / - + ----- |
\\/ 2 4 /
$$x_{14} = - \pi + \operatorname{atan}{\left(\frac{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}} \right)} + i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)$$
x14 = -pi + atan(sqrt(1/2 - sqrt(2)/4)/sqrt(sqrt(2)/4 + 1/2)) + i*(-log(2^(1/4)) + log(2)/4)
Respuesta numérica
[src]
x1 = -9.73893722612836
x2 = 61.8893752757189
x3 = -87.6504350351552
x4 = 46.18141200777
x5 = -55.3705705195201
x6 = 56.2345084992573
x7 = 26.0752190247953
x8 = 93.9336203423348
x9 = -23.9546439836222
x10 = 54.3495529071034
x11 = -58.1194640914112
x12 = 66.2876049907446
x13 = -70.0575161750524
x14 = 48.3019870489431
x15 = 33.6150413934108
x16 = -5.96902604182061
x17 = -41.7831822927443
x18 = -60.0044196835651
x19 = -51.8362787842316
x20 = -89.9280897090078
x21 = 76.5763209312512
x22 = 88.2787535658732
x23 = 10.3672557568463
x24 = -99.5884871187965
x25 = 7.85398163397448
x26 = -48.0663675999238
x27 = 17.9070781254618
x28 = 58.1194640914112
x29 = 60.0044196835651
x30 = -49.3230046613598
x31 = 38.0132711084365
x32 = -4.08407044966673
x33 = 39.8982267005904
x34 = 95.42587685279
x35 = -95.8185759344887
x36 = 22.3053078404875
x37 = -1.96349540849362
x38 = 29.845130209103
x39 = 98.3318500573605
x40 = 83.8805238508475
x41 = -11.6238928182822
x42 = 80.1106126665397
x43 = 64.009950316892
x44 = 16.0221225333079
x45 = -31.7300858012569
x46 = 12.2522113490002
x47 = 20.0276531666349
x48 = 81.9955682586936
x49 = -80.1106126665397
x50 = -29.845130209103
x51 = 663.818527703523
x52 = -61.8893752757189
x53 = -53.7212343763855
x54 = 92.2842841992002
x55 = -81.9955682586936
x56 = 44.2964564156161
x57 = -93.8550805259951
x58 = -39.8982267005904
x59 = -78.2256570743859
x60 = 73.4347282776614
x61 = 2.19911485751286
x62 = -85.7654794430014
x63 = 49.9513231920777
x64 = -43.6681378848981
x65 = 14.1371669411541
x66 = 3.45575191894877
x67 = 100.216805649514
x68 = 70.2931356240716
x69 = -16.0221225333079
x70 = -36.1283155162826
x71 = 0.314159265358979
x72 = -18.5353966561798
x73 = 90.1637091580271
x74 = -67.9369411338793
x75 = 71.9424717672063
x76 = -21.6769893097696
x77 = 78.2256570743859
x78 = 36.1283155162826
x79 = -26.0752190247953
x80 = -14.1371669411541
x81 = -27.096236637212
x82 = -45.9457925587507
x83 = 27.9601746169492
x84 = 24.1902634326414
x85 = -19.7920337176157
x86 = 68.1725605828985
x87 = -75.712382951514
x88 = 86.0010988920206
x89 = -63.7743308678728
x90 = -83.8805238508475
x91 = -7.85398163397448
x92 = 42.0188017417635
x93 = -71.3141532364883
x94 = 5.96902604182061
x95 = -38.0132711084365
x96 = -73.8274273593601
x97 = -97.7035315266426
x98 = 34.2433599241287
x99 = -92.0486647501809
x100 = -65.6592864600267
x100 = -65.6592864600267