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- La ecuación:
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Ecuación sin(x)=-1
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Ecuación x^4-4*x^3-2*x^2+12*x+9=0
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Ecuación (x-4)^2+(x+9)^2=2*x^2
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Ecuación 4x^2-12x+9=0
- Expresar {x} en función de y en la ecuación:
- 1*x-6*y=-19
- -1*x-19*y=-10
- 18*x+19*y=7
- 18*x+14*y=-11
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Expresiones idénticas
- log2((sin2x+2sinx+cosx+ uno)/(2sinx+ uno))= cero
- logaritmo de 2(( seno de 2x más 2 seno de x más coseno de x más 1) dividir por (2 seno de x más 1)) es igual a 0
- logaritmo de 2(( seno de 2x más 2 seno de x más coseno de x más uno) dividir por (2 seno de x más uno)) es igual a cero
- log2sin2x+2sinx+cosx+1/2sinx+1=0
- log2((sin2x+2sinx+cosx+1)/(2sinx+1))=O
- log2((sin2x+2sinx+cosx+1) dividir por (2sinx+1))=0
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Expresiones semejantes
- log2((sin2x+2sinx-cosx+1)/(2sinx+1))=0
- log2((sin2x-2sinx+cosx+1)/(2sinx+1))=0
- log2((sin2x+2sinx+cosx-1)/(2sinx+1))=0
- log2((sin2x+2sinx+cosx+1)/(2sinx-1))=0
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Expresiones con funciones
- cosx
- cosx=-6/5
- cosx/2+1=0
- cosx×(1-cosx)=0
- Cosx4-cos2x=1
- cosx/7=-1
log2((sin2x+2sinx+cosx+1)/(2sinx+1))=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/sin(2*x) + 2*sin(x) + cos(x) + 1\
log|--------------------------------|
\ 2*sin(x) + 1 /
------------------------------------- = 0
log(2)
$$\frac{\log{\left(\frac{\left(\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) + \cos{\left(x \right)}\right) + 1}{2 \sin{\left(x \right)} + 1} \right)}}{\log{\left(2 \right)}} = 0$$
Solución detallada
Tenemos la ecuación
$$\frac{\log{\left(\frac{\left(\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) + \cos{\left(x \right)}\right) + 1}{2 \sin{\left(x \right)} + 1} \right)}}{\log{\left(2 \right)}} = 0$$
cambiamos
$$\frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{\log{\left(2 \right)}} - 1 = 0$$
$$\frac{\log{\left(\frac{\left(\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) + \cos{\left(x \right)}\right) + 1}{2 \sin{\left(x \right)} + 1} \right)}}{\log{\left(2 \right)}} - 1 = 0$$
Sustituimos
$$w = \log{\left(\frac{2 \sin{\left(x \right)}}{2 \sin{\left(x \right)} + 1} + \frac{\sin{\left(2 x \right)}}{2 \sin{\left(x \right)} + 1} + \frac{\cos{\left(x \right)}}{2 \sin{\left(x \right)} + 1} + \frac{1}{2 \sin{\left(x \right)} + 1} \right)}$$
Tenemos la ecuación:
$$\frac{\log{\left(\frac{\left(\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) + \cos{\left(x \right)}\right) + 1}{2 \sin{\left(x \right)} + 1} \right)}}{\log{\left(2 \right)}} - 1 = 0$$
Usamos la regla de proporciones:
De a1/b1 = a2/b2 se deduce a1*b2 = a2*b1,
En nuestro caso
signo obtendremos la ecuación
$$\log{\left(\frac{2 \sin{\left(x \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)} + 1}{2 \sin{\left(x \right)} + 1} \right)} = \log{\left(2 \right)}$$
$$\log{\left(\frac{2 \sin{\left(x \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)} + 1}{2 \sin{\left(x \right)} + 1} \right)} = \log{\left(2 \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
Abrimos los paréntesis en el miembro derecho de la ecuación
Esta ecuación no tiene soluciones
hacemos cambio inverso
$$\log{\left(\frac{2 \sin{\left(x \right)}}{2 \sin{\left(x \right)} + 1} + \frac{\sin{\left(2 x \right)}}{2 \sin{\left(x \right)} + 1} + \frac{\cos{\left(x \right)}}{2 \sin{\left(x \right)} + 1} + \frac{1}{2 \sin{\left(x \right)} + 1} \right)} = w$$
sustituimos w:
$$\frac{\log{\left(\frac{\left(\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) + \cos{\left(x \right)}\right) + 1}{2 \sin{\left(x \right)} + 1} \right)}}{\log{\left(2 \right)}} = 0$$
cambiamos
$$\frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{\log{\left(2 \right)}} - 1 = 0$$
$$\frac{\log{\left(\frac{\left(\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) + \cos{\left(x \right)}\right) + 1}{2 \sin{\left(x \right)} + 1} \right)}}{\log{\left(2 \right)}} - 1 = 0$$
Sustituimos
$$w = \log{\left(\frac{2 \sin{\left(x \right)}}{2 \sin{\left(x \right)} + 1} + \frac{\sin{\left(2 x \right)}}{2 \sin{\left(x \right)} + 1} + \frac{\cos{\left(x \right)}}{2 \sin{\left(x \right)} + 1} + \frac{1}{2 \sin{\left(x \right)} + 1} \right)}$$
Tenemos la ecuación:
$$\frac{\log{\left(\frac{\left(\left(2 \sin{\left(x \right)} + \sin{\left(2 x \right)}\right) + \cos{\left(x \right)}\right) + 1}{2 \sin{\left(x \right)} + 1} \right)}}{\log{\left(2 \right)}} - 1 = 0$$
Usamos la regla de proporciones:
De a1/b1 = a2/b2 se deduce a1*b2 = a2*b1,
En nuestro caso
a1 = log((1 + 2*sin(x) + cos(x) + sin(2*x))/(1 + 2*sin(x)))
b1 = log(2)
a2 = 1
b2 = 1
signo obtendremos la ecuación
$$\log{\left(\frac{2 \sin{\left(x \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)} + 1}{2 \sin{\left(x \right)} + 1} \right)} = \log{\left(2 \right)}$$
$$\log{\left(\frac{2 \sin{\left(x \right)} + \sin{\left(2 x \right)} + \cos{\left(x \right)} + 1}{2 \sin{\left(x \right)} + 1} \right)} = \log{\left(2 \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
log1+2*sin+x + cosx + sin2*x)/1+/2*sin+/x)) = log(2)
Abrimos los paréntesis en el miembro derecho de la ecuación
log1+2*sin+x + cosx + sin2*x)/1+/2*sin+/x)) = log2
Esta ecuación no tiene soluciones
hacemos cambio inverso
$$\log{\left(\frac{2 \sin{\left(x \right)}}{2 \sin{\left(x \right)} + 1} + \frac{\sin{\left(2 x \right)}}{2 \sin{\left(x \right)} + 1} + \frac{\cos{\left(x \right)}}{2 \sin{\left(x \right)} + 1} + \frac{1}{2 \sin{\left(x \right)} + 1} \right)} = w$$
sustituimos w:
Respuesta numérica
[src]
x1 = 1.5707963267949
x2 = 39.2699081698724
x3 = -39.2699081698724
x4 = 14.1371669411541
x5 = -70.6858347057703
x6 = 32.9867228626928
x7 = 61.261056745001
x8 = 36.1283155162826
x9 = -61.261056745001
x10 = -105.243353895258
x11 = -36.1283155162826
x12 = -48.6946861306418
x13 = 7.85398163397448
x14 = 70.6858347057703
x15 = -80.1106126665397
x16 = 42.4115008234622
x17 = 51.8362787842316
x18 = -98.9601685880785
x19 = 80.1106126665397
x20 = -64.4026493985908
x21 = -29.845130209103
x22 = 98.9601685880785
x23 = 83.2522053201295
x24 = -89.5353906273091
x25 = -86.3937979737193
x26 = -10.9955742875643
x27 = 17.2787595947439
x28 = -26.7035375555132
x29 = -54.9778714378214
x30 = -92.6769832808989
x31 = 89.5353906273091
x32 = 58.1194640914112
x33 = 4.71238898038469
x34 = 20.4203522483337
x35 = 73.8274273593601
x36 = -67.5442420521806
x37 = 45.553093477052
x38 = -58.1194640914112
x39 = -51.8362787842316
x40 = -83.2522053201295
x41 = -76.9690200129499
x42 = -14.1371669411541
x43 = -73.8274273593601
x44 = 92.6769832808989
x45 = -20.4203522483337
x46 = 64.4026493985908
x47 = 95.8185759344887
x48 = 67.5442420521806
x49 = 54.9778714378214
x50 = 48.6946861306418
x51 = -4.71238898038469
x52 = 76.9690200129499
x53 = -7.85398163397448
x54 = -45.553093477052
x55 = -95.8185759344887
x56 = 29.845130209103
x57 = 26.7035375555132
x58 = -17.2787595947439
x59 = -32.9867228626928
x60 = -1.5707963267949
x61 = 23.5619449019235
x62 = 10.9955742875643
x63 = 86.3937979737193
x64 = -23.5619449019235
x65 = -42.4115008234622
x65 = -42.4115008234622