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- La ecuación:
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Ecuación x^2-6x+9=0
-
Ecuación (x-11)^4=(x+3)^4
-
Ecuación √(x^2-1)^3=2*x
-
Ecuación -x/12+x=55/12
- Expresar {x} en función de y en la ecuación:
- 18*x-11*y=2
- 12*x-14*y=20
- -3*x-20*y=-13
- -16*x+14*y=-9
-
Expresiones idénticas
- cosx((cosx)^ dos -sinx)= cero
- coseno de x(( coseno de x) al cuadrado menos seno de x) es igual a 0
- coseno de x(( coseno de x) en el grado dos menos seno de x) es igual a cero
- cosx((cosx)2-sinx)=0
- cosxcosx2-sinx=0
- cosx((cosx)²-sinx)=0
- cosx((cosx) en el grado 2-sinx)=0
- cosxcosx^2-sinx=0
- cosx((cosx)^2-sinx)=O
-
Expresiones semejantes
- cosx((cosx)^2+sinx)=0
-
Expresiones con funciones
- cosx
- cosx-lnx=0
- cosx=0,445
- cosx=-sinx
- cosx2=√3/2
- cosx+2sin(pi+x)-sin(pi/2-x)=-1
- cosx
- cosx-lnx=0
- cosx=0,445
- cosx=-sinx
- cosx2=√3/2
- cosx+2sin(pi+x)-sin(pi/2-x)=-1
- sinx
- sinx=0
- sinx=√3/2
- sinx/2=1/2
- sinx=2
- sinx/1+cosx=1-cosx
cosx((cosx)^2-sinx)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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/ 2 \ cos(x)*\cos (x) - sin(x)/ = 0
$$\left(- \sin{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)} = 0$$
Respuesta rápida
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-pi
x1 = ----
2
$$x_{1} = - \frac{\pi}{2}$$
pi
x2 = --
2
$$x_{2} = \frac{\pi}{2}$$
/ / ___________\\ / / ___________\\
| | ___ ___ / ___ || | | ___ ___ / ___ ||
| | 1 \/ 5 \/ 2 *\/ 1 - \/ 5 || | | 1 \/ 5 \/ 2 *\/ 1 - \/ 5 ||
x3 = - 2*re|atan|- - + ----- + --------------------|| - 2*I*im|atan|- - + ----- + --------------------||
\ \ 2 2 2 // \ \ 2 2 2 //
$$x_{3} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)}$$
/ ___________\
| ___ ___ / ___ |
|1 \/ 5 \/ 2 *\/ 1 + \/ 5 |
x4 = 2*atan|- + ----- + --------------------|
\2 2 2 /
$$x_{4} = 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{2} \right)}$$
/ / ___________\\ / / ___________\\
| | ___ ___ / ___ || | | ___ ___ / ___ ||
| |1 \/ 5 \/ 2 *\/ 1 - \/ 5 || | |1 \/ 5 \/ 2 *\/ 1 - \/ 5 ||
x5 = 2*re|atan|- - ----- + --------------------|| + 2*I*im|atan|- - ----- + --------------------||
\ \2 2 2 // \ \2 2 2 //
$$x_{5} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{5}}{2} + \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{5}}{2} + \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)}$$
/ ___________\
| ___ ___ / ___ |
|1 \/ 5 \/ 2 *\/ 1 + \/ 5 |
x6 = 2*atan|- + ----- - --------------------|
\2 2 2 /
$$x_{6} = 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{2} + \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
x6 = 2*atan(-sqrt(2)*sqrt(1 + sqrt(5))/2 + 1/2 + sqrt(5)/2)
Suma y producto de raíces
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suma
/ / ___________\\ / / ___________\\ / ___________\ / / ___________\\ / / ___________\\ / ___________\
| | ___ ___ / ___ || | | ___ ___ / ___ || | ___ ___ / ___ | | | ___ ___ / ___ || | | ___ ___ / ___ || | ___ ___ / ___ |
pi pi | | 1 \/ 5 \/ 2 *\/ 1 - \/ 5 || | | 1 \/ 5 \/ 2 *\/ 1 - \/ 5 || |1 \/ 5 \/ 2 *\/ 1 + \/ 5 | | |1 \/ 5 \/ 2 *\/ 1 - \/ 5 || | |1 \/ 5 \/ 2 *\/ 1 - \/ 5 || |1 \/ 5 \/ 2 *\/ 1 + \/ 5 |
- -- + -- + - 2*re|atan|- - + ----- + --------------------|| - 2*I*im|atan|- - + ----- + --------------------|| + 2*atan|- + ----- + --------------------| + 2*re|atan|- - ----- + --------------------|| + 2*I*im|atan|- - ----- + --------------------|| + 2*atan|- + ----- - --------------------|
2 2 \ \ 2 2 2 // \ \ 2 2 2 // \2 2 2 / \ \2 2 2 // \ \2 2 2 // \2 2 2 /
$$\left(\left(2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{2} \right)} + \left(\left(- \frac{\pi}{2} + \frac{\pi}{2}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)}\right)\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{5}}{2} + \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{5}}{2} + \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)}\right)\right) + 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{2} + \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
=
/ / ___________\\ / ___________\ / ___________\ / / ___________\\ / / ___________\\ / / ___________\\
| | ___ ___ / ___ || | ___ ___ / ___ | | ___ ___ / ___ | | | ___ ___ / ___ || | | ___ ___ / ___ || | | ___ ___ / ___ ||
| | 1 \/ 5 \/ 2 *\/ 1 - \/ 5 || |1 \/ 5 \/ 2 *\/ 1 + \/ 5 | |1 \/ 5 \/ 2 *\/ 1 + \/ 5 | | |1 \/ 5 \/ 2 *\/ 1 - \/ 5 || | | 1 \/ 5 \/ 2 *\/ 1 - \/ 5 || | |1 \/ 5 \/ 2 *\/ 1 - \/ 5 ||
- 2*re|atan|- - + ----- + --------------------|| + 2*atan|- + ----- + --------------------| + 2*atan|- + ----- - --------------------| + 2*re|atan|- - ----- + --------------------|| - 2*I*im|atan|- - + ----- + --------------------|| + 2*I*im|atan|- - ----- + --------------------||
\ \ 2 2 2 // \2 2 2 / \2 2 2 / \ \2 2 2 // \ \ 2 2 2 // \ \2 2 2 //
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{5}}{2} + \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)} + 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{2} + \frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{2} \right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{5}}{2} + \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)}$$
producto
/ / / ___________\\ / / ___________\\\ / ___________\ / / / ___________\\ / / ___________\\\ / ___________\
| | | ___ ___ / ___ || | | ___ ___ / ___ ||| | ___ ___ / ___ | | | | ___ ___ / ___ || | | ___ ___ / ___ ||| | ___ ___ / ___ |
-pi pi | | | 1 \/ 5 \/ 2 *\/ 1 - \/ 5 || | | 1 \/ 5 \/ 2 *\/ 1 - \/ 5 ||| |1 \/ 5 \/ 2 *\/ 1 + \/ 5 | | | |1 \/ 5 \/ 2 *\/ 1 - \/ 5 || | |1 \/ 5 \/ 2 *\/ 1 - \/ 5 ||| |1 \/ 5 \/ 2 *\/ 1 + \/ 5 |
----*--*|- 2*re|atan|- - + ----- + --------------------|| - 2*I*im|atan|- - + ----- + --------------------|||*2*atan|- + ----- + --------------------|*|2*re|atan|- - ----- + --------------------|| + 2*I*im|atan|- - ----- + --------------------|||*2*atan|- + ----- - --------------------|
2 2 \ \ \ 2 2 2 // \ \ 2 2 2 /// \2 2 2 / \ \ \2 2 2 // \ \2 2 2 /// \2 2 2 /
$$- \frac{\pi}{2} \frac{\pi}{2} \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)}\right) 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{2} \right)} \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{5}}{2} + \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{5}}{2} + \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)}\right) 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{2} + \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
=
/ / / ___________\\ / / ___________\\\ / / / ___________\\ / / ___________\\\ / ___________\ / ___________\
| | | ___ ___ / ___ || | | ___ ___ / ___ ||| | | | ___ ___ / ___ || | | ___ ___ / ___ ||| | ___ ___ / ___ | | ___ ___ / ___ |
2 | | |1 \/ 5 \/ 2 *\/ 1 - \/ 5 || | |1 \/ 5 \/ 2 *\/ 1 - \/ 5 ||| | | | 1 \/ 5 \/ 2 *\/ 1 - \/ 5 || | | 1 \/ 5 \/ 2 *\/ 1 - \/ 5 ||| |1 \/ 5 \/ 2 *\/ 1 + \/ 5 | |1 \/ 5 \/ 2 *\/ 1 + \/ 5 |
4*pi *|I*im|atan|- - ----- + --------------------|| + re|atan|- - ----- + --------------------|||*|I*im|atan|- - + ----- + --------------------|| + re|atan|- - + ----- + --------------------|||*atan|- + ----- + --------------------|*atan|- + ----- - --------------------|
\ \ \2 2 2 // \ \2 2 2 /// \ \ \ 2 2 2 // \ \ 2 2 2 /// \2 2 2 / \2 2 2 /
$$4 \pi^{2} \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{5}}{2} + \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{5}}{2} + \frac{1}{2} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{2} \right)}\right)}\right) \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} + \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{2} \right)} \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{1 + \sqrt{5}}}{2} + \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
4*pi^2*(i*im(atan(1/2 - sqrt(5)/2 + sqrt(2)*sqrt(1 - sqrt(5))/2)) + re(atan(1/2 - sqrt(5)/2 + sqrt(2)*sqrt(1 - sqrt(5))/2)))*(i*im(atan(-1/2 + sqrt(5)/2 + sqrt(2)*sqrt(1 - sqrt(5))/2)) + re(atan(-1/2 + sqrt(5)/2 + sqrt(2)*sqrt(1 - sqrt(5))/2)))*atan(1/2 + sqrt(5)/2 + sqrt(2)*sqrt(1 + sqrt(5))/2)*atan(1/2 + sqrt(5)/2 - sqrt(2)*sqrt(1 + sqrt(5))/2)
Respuesta numérica
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x1 = -64.4026493985908
x2 = -23.5619449019235
x3 = -55.8824283321238
x4 = 61.261056745001
x5 = -29.845130209103
x6 = -60.3564998506986
x7 = 8.75853852827686
x8 = 42.4115008234622
x9 = 4.71238898038469
x10 = -18.1833164890462
x11 = 36.1283155162826
x12 = 10.9955742875643
x13 = 23.5619449019235
x14 = 82.3476484258271
x15 = 54.9778714378214
x16 = -11.9001311818667
x17 = -80.1106126665397
x18 = 33.8912797569952
x19 = 86.3937979737193
x20 = -43.3160577177646
x21 = 40.1744650641748
x22 = 64.4026493985908
x23 = -83.2522053201295
x24 = 84.1567622144319
x25 = 98.9601685880785
x26 = -95.8185759344887
x27 = -1.5707963267949
x28 = 73.8274273593601
x29 = -39.2699081698724
x30 = 67.5442420521806
x31 = -32.9867228626928
x32 = 77.8735769072523
x33 = -3.80783208608231
x34 = 111.526539202438
x35 = 0.666239432492515
x36 = 44.6485365827496
x37 = -99.8647254823809
x38 = -51.8362787842316
x39 = 58.1194640914112
x40 = -98.0556116937761
x41 = 2.47535322109728
x42 = -73.8274273593601
x43 = 51.8362787842316
x44 = -62.1656136393034
x45 = 69.781277811468
x46 = -45.553093477052
x47 = 29.845130209103
x48 = -87.2983548680217
x49 = -91.7724263865965
x50 = 80.1106126665397
x51 = -58.1194640914112
x52 = 25.7989806612109
x53 = -5.61694587468707
x54 = -36.1283155162826
x55 = 90.4399475216115
x56 = 38.36535127557
x57 = -16.3742027004415
x58 = -47.7901292363394
x59 = -67.5442420521806
x60 = -7.85398163397448
x61 = 48.6946861306418
x62 = 46.4576503713544
x63 = 63.4980925042884
x64 = 32.0821659683904
x65 = 71.5903916000727
x66 = 7.85398163397448
x67 = -14.1371669411541
x68 = 88.6308337330067
x69 = -4.71238898038469
x70 = 52.740835678534
x71 = 19.5157953540313
x72 = -41.5069439291598
x73 = 14.1371669411541
x74 = -35.2237586219802
x75 = -49.5992430249442
x76 = 27.6080944498156
x77 = 20.4203522483337
x78 = -70.6858347057703
x79 = -26.7035375555132
x80 = -54.073314543519
x81 = 95.8185759344887
x82 = 76.0644631186476
x83 = -89.5353906273091
x84 = 17.2787595947439
x85 = -93.5815401752013
x86 = -10.0910173932619
x87 = 92.6769832808989
x88 = -76.9690200129499
x89 = -20.4203522483337
x89 = -20.4203522483337