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Ecuación x^3+3x^2-x-3=0
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Ecuación x^3-6x^2+11x-6=0
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Ecuación x/4+x=12
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Ecuación x+4=-1
- Expresar {x} en función de y en la ecuación:
- 9*x-1*y=17
- 10*x-2*y=11
- -18*x-13*y=2
- -12*x-8*y=13
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Expresiones idénticas
- sin(x)^(dos)- dos *sin(x)- tres = cero
- seno de (x) en el grado (2) menos 2 multiplicar por seno de (x) menos 3 es igual a 0
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- sin(x)(2)-2*sin(x)-3=0
- sinx2-2*sinx-3=0
- sin(x)^(2)-2sin(x)-3=0
- sin(x)(2)-2sin(x)-3=0
- sinx2-2sinx-3=0
- sinx^2-2sinx-3=0
- sin(x)^(2)-2*sin(x)-3=O
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Expresiones semejantes
- sin(x)^(2)+2*sin(x)-3=0
- sin(x)^(2)-2*sin(x)+3=0
- sinx^(2)-2*sinx-3=0
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Expresiones con funciones
- Seno sin
- sin(x)=1.5
- sin(sin(x))=1
- sin(x)=-0.5
- sin(-x)=1/2
- sin(x)=4/3
- Seno sin
- sin(x)=1.5
- sin(sin(x))=1
- sin(x)=-0.5
- sin(-x)=1/2
- sin(x)=4/3
sin(x)^(2)-2*sin(x)-3=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 sin (x) - 2*sin(x) - 3 = 0
$$\left(\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)}\right) - 3 = 0$$
Solución detallada
Tenemos la ecuación
$$\left(\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)}\right) - 3 = 0$$
cambiamos
$$\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} - 3 = 0$$
$$\left(\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)}\right) - 3 = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 1$$
$$b = -2$$
$$c = -3$$
, entonces
Como D > 0 la ecuación tiene dos raíces.
o
$$w_{1} = 3$$
$$w_{2} = -1$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(3 \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(3 \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$x_{2} = 2 \pi n - \frac{\pi}{2}$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{3} = 2 \pi n + \pi - \operatorname{asin}{\left(3 \right)}$$
$$x_{3} = 2 \pi n + \pi - \operatorname{asin}{\left(3 \right)}$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
$$x_{4} = 2 \pi n + \frac{3 \pi}{2}$$
$$\left(\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)}\right) - 3 = 0$$
cambiamos
$$\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} - 3 = 0$$
$$\left(\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)}\right) - 3 = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Es la ecuación de la forma
a*w^2 + b*w + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 1$$
$$b = -2$$
$$c = -3$$
, entonces
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-3) = 16
Como D > 0 la ecuación tiene dos raíces.
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
o
$$w_{1} = 3$$
$$w_{2} = -1$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(3 \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(3 \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$x_{2} = 2 \pi n - \frac{\pi}{2}$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{3} = 2 \pi n + \pi - \operatorname{asin}{\left(3 \right)}$$
$$x_{3} = 2 \pi n + \pi - \operatorname{asin}{\left(3 \right)}$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
$$x_{4} = 2 \pi n + \frac{3 \pi}{2}$$
Suma y producto de raíces
[src]
suma
pi 3*pi - -- + ---- + pi - re(asin(3)) - I*im(asin(3)) + I*im(asin(3)) + re(asin(3)) 2 2
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) + \left(\left(- \frac{\pi}{2} + \frac{3 \pi}{2}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)\right)$$
=
2*pi
$$2 \pi$$
producto
-pi 3*pi ----*----*(pi - re(asin(3)) - I*im(asin(3)))*(I*im(asin(3)) + re(asin(3))) 2 2
$$- \frac{\pi}{2} \frac{3 \pi}{2} \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)$$
=
2
3*pi *(I*im(asin(3)) + re(asin(3)))*(-pi + I*im(asin(3)) + re(asin(3)))
-----------------------------------------------------------------------
4
$$\frac{3 \pi^{2} \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)}{4}$$
3*pi^2*(i*im(asin(3)) + re(asin(3)))*(-pi + i*im(asin(3)) + re(asin(3)))/4
Respuesta rápida
[src]
-pi
x1 = ----
2
$$x_{1} = - \frac{\pi}{2}$$
3*pi
x2 = ----
2
$$x_{2} = \frac{3 \pi}{2}$$
x3 = pi - re(asin(3)) - I*im(asin(3))
$$x_{3} = - \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}$$
x4 = I*im(asin(3)) + re(asin(3))
$$x_{4} = \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}$$
x4 = re(asin(3)) + i*im(asin(3))
Respuesta numérica
[src]
x1 = -51.8362786895378
x2 = 48.6946859120413
x3 = 17.2787599090696
x4 = 80.1106131400977
x5 = -1.57079643080582
x6 = 73.827427591263
x7 = 4.71238923181769
x8 = 29.8451303217623
x9 = -39.2699084013107
x10 = -58.119463652249
x11 = 48.6946863700612
x12 = -20.4203520186622
x13 = -70.6858350312864
x14 = -14.1371668194089
x15 = 86.3937976360352
x16 = -64.4026496039382
x17 = 92.6769835070253
x18 = 882955.610865625
x19 = 4.71238875528975
x20 = -83.2522055577573
x21 = -83.2522051037983
x22 = -64.4026491754768
x23 = 98.9601682894894
x24 = -14.1371665766936
x25 = 61.261057062553
x26 = 117.809725233756
x27 = 212.057503588662
x28 = 67.5442422944741
x29 = -20.4203524688757
x30 = 23.5619446676752
x31 = 42.4115007283113
x32 = 42.4115009058131
x33 = -83.2522050480464
x34 = 92.6769830689412
x35 = 54.9778717720118
x36 = 42.4115005526819
x37 = -133.517687838813
x38 = 10.9955746230205
x39 = -26.7035372446302
x40 = 73.8274274813446
x41 = 54.9778711353875
x42 = -1.57079653638307
x43 = -39.2699079075865
x44 = 67.5442418055755
x45 = 17.2787592660486
x46 = -39.2699076412407
x47 = -108.38494727522
x48 = -139.800873467486
x49 = -32.9867225263379
x50 = 61.2610564153358
x51 = -14.1371668381663
x52 = -76.9690203256113
x53 = 10.9955739814993
x54 = 98.9601689206173
x55 = 36.1283157033748
x56 = -89.5353907308516
x57 = -26.703537882833
x58 = -76.9690196760468
x59 = 86.3937978876249
x60 = -45.5530936309972
x61 = -164.933614398177
x62 = -58.1194639985047
x63 = -32.9867231721691
x64 = 4.71238886235498
x65 = -95.8185758680893
x66 = -45.5530935897427
x67 = -89.5353907485116
x68 = -7.85398149759801
x69 = 23.5619451379884
x70 = -70.6858343985417
x71 = 29.845130504401
x71 = 29.845130504401
Gráfico