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- La ecuación:
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Ecuación y^2-5*y=0
-
Ecuación 49x^3+14x^2+x=0
-
Ecuación x-12=0
-
Ecuación (x-3)/(x+1)=0
- Expresar {x} en función de y en la ecuación:
- -16*x+3*y=17
- 18*x-14*y=-2
- 18*x+19*y=10
- 11*x-6*y=5
-
Expresiones idénticas
- cinco *sin(x)^(dos)= tres - catorce *sin(x)
- 5 multiplicar por seno de (x) en el grado (2) es igual a 3 menos 14 multiplicar por seno de (x)
- cinco multiplicar por seno de (x) en el grado (dos) es igual a tres menos cotangente de angente de orce multiplicar por seno de (x)
- 5*sin(x)(2)=3-14*sin(x)
- 5*sinx2=3-14*sinx
- 5sin(x)^(2)=3-14sin(x)
- 5sin(x)(2)=3-14sin(x)
- 5sinx2=3-14sinx
- 5sinx^2=3-14sinx
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Expresiones semejantes
- 5*sin(x)^(2)=3+14*sin(x)
- 5*sinx^(2)=3-14*sinx
-
Expresiones con funciones
- Seno sin
- sin(x/2-pi/6)+1=0
- sin^4(3x)=0
- sin(x)=530×10^9/21
- sin(x)cos(x)=1/16
- sin(x)*2=1/4
- Seno sin
- sin(x/2-pi/6)+1=0
- sin^4(3x)=0
- sin(x)=530×10^9/21
- sin(x)cos(x)=1/16
- sin(x)*2=1/4
5*sin(x)^(2)=3-14*sin(x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 5*sin (x) = 3 - 14*sin(x)
$$5 \sin^{2}{\left(x \right)} = 3 - 14 \sin{\left(x \right)}$$
Solución detallada
Tenemos la ecuación
$$5 \sin^{2}{\left(x \right)} = 3 - 14 \sin{\left(x \right)}$$
cambiamos
$$5 \sin^{2}{\left(x \right)} + 14 \sin{\left(x \right)} - 3 = 0$$
$$\left(14 \sin{\left(x \right)} - 3\right) + 5 \sin^{2}{\left(x \right)} = 0$$
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
$$a = 5$$
$$b = 14$$
$$c = -3$$
, entonces
Como D > 0 la ecuación tiene dos raíces.
o
$$w_{1} = \frac{1}{5}$$
$$w_{2} = -3$$
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:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(-3 \right)}$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(3 \right)}$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi$$
$$x_{4} = 2 \pi n + \pi - \operatorname{asin}{\left(-3 \right)}$$
$$x_{4} = 2 \pi n + \pi + \operatorname{asin}{\left(3 \right)}$$
$$5 \sin^{2}{\left(x \right)} = 3 - 14 \sin{\left(x \right)}$$
cambiamos
$$5 \sin^{2}{\left(x \right)} + 14 \sin{\left(x \right)} - 3 = 0$$
$$\left(14 \sin{\left(x \right)} - 3\right) + 5 \sin^{2}{\left(x \right)} = 0$$
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
$$a = 5$$
$$b = 14$$
$$c = -3$$
, entonces
D = b^2 - 4 * a * c =
(14)^2 - 4 * (5) * (-3) = 256
Como D > 0 la ecuación tiene dos raíces.
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
o
$$w_{1} = \frac{1}{5}$$
$$w_{2} = -3$$
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:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(-3 \right)}$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(3 \right)}$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi$$
$$x_{4} = 2 \pi n + \pi - \operatorname{asin}{\left(-3 \right)}$$
$$x_{4} = 2 \pi n + \pi + \operatorname{asin}{\left(3 \right)}$$
Respuesta rápida
[src]
x1 = pi - asin(1/5)
$$x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
x2 = asin(1/5)
$$x_{2} = \operatorname{asin}{\left(\frac{1}{5} \right)}$$
x3 = pi + I*im(asin(3)) + re(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 = -re(asin(3)) - I*im(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))
Suma y producto de raíces
[src]
suma
pi - asin(1/5) + asin(1/5) + pi + I*im(asin(3)) + re(asin(3)) + -re(asin(3)) - I*im(asin(3))
$$\left(\left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \left(\pi - \operatorname{asin}{\left(\frac{1}{5} \right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)$$
=
2*pi
$$2 \pi$$
producto
(pi - asin(1/5))*asin(1/5)*(pi + I*im(asin(3)) + re(asin(3)))*(-re(asin(3)) - I*im(asin(3)))
$$\left(\pi - \operatorname{asin}{\left(\frac{1}{5} \right)}\right) \operatorname{asin}{\left(\frac{1}{5} \right)} \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)$$
=
-(pi - asin(1/5))*(I*im(asin(3)) + re(asin(3)))*(pi + I*im(asin(3)) + re(asin(3)))*asin(1/5)
$$- \left(\pi - \operatorname{asin}{\left(\frac{1}{5} \right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) \operatorname{asin}{\left(\frac{1}{5} \right)}$$
-(pi - asin(1/5))*(i*im(asin(3)) + re(asin(3)))*(pi + i*im(asin(3)) + re(asin(3)))*asin(1/5)
Respuesta numérica
[src]
x1 = 31.6172844566883
x2 = -56.3473098438259
x3 = -43.7809392294668
x4 = 21.7897906543382
x5 = 90.9048290333137
x6 = 40.639346575877
x7 = -85.0243595677148
x8 = -41.0420624174576
x9 = -263.692424980752
x10 = -22.1925064959189
x11 = -53.6084330318168
x12 = 12.7677285351495
x13 = 6.48454322796992
x14 = 97.1880143404933
x15 = -72.4579889533556
x16 = 69.3163962997658
x17 = -12.3650126935688
x18 = -68.9136804581851
x19 = 94.4491375284841
x20 = 46.9225318830566
x21 = -15.9093211887393
x22 = -3.34295057438012
x23 = 65.7720878045953
x24 = 72.0552731117749
x25 = 2.94023473279946
x26 = 0.201357920790331
x27 = -62.6304951510055
x28 = -37.4977539222872
x29 = 81.882766914125
x30 = 88.1659522213045
x31 = -91.3075448748943
x32 = 15.5066053471586
x33 = 19.0509138423291
x34 = -31.2145686151076
x35 = -138.028718837161
x36 = 63.0332109925862
x37 = -59.8916183389964
x38 = -24.931383307928
x39 = 50.466840378227
x40 = -78.7411742605352
x41 = 75.5995816069454
x42 = -66.174803646176
x43 = 9.22342003997905
x44 = 100.732322835664
x45 = 56.7500256854066
x46 = -147.856212639511
x47 = -28.4756918030985
x48 = 1517.18789376308
x49 = 78.3384584189545
x50 = 37.9004697638678
x51 = -94.0464216869035
x52 = 84.6216437261341
x53 = -9.62613588155971
x54 = -97.5907301820739
x55 = 59.4889024974157
x56 = -100.329606994083
x57 = -50.0641245366464
x58 = -18.6481980007484
x59 = -34.7588771102781
x60 = -81.4800510725443
x61 = 53.2057171902362
x62 = -87.7632363797239
x63 = 34.3561612686974
x64 = 28.0729759615178
x65 = -6.08182738638926
x66 = 25.3340991495087
x67 = 44.1836550710474
x68 = -47.3252477246372
x69 = -75.1968657653647
x69 = -75.1968657653647