Sr Examen

Otras calculadoras

tan^2x=2 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
   2       
tan (x) = 2
tan⁡2(x)=2\tan^{2}{\left(x \right)} = 2
Simplificar
Solución detallada
Tenemos la ecuación
tan⁡2(x)=2\tan^{2}{\left(x \right)} = 2
cambiamos
tan⁡2(x)−2=0\tan^{2}{\left(x \right)} - 2 = 0
tan⁡2(x)−2=0\tan^{2}{\left(x \right)} - 2 = 0
Sustituimos
w=tan⁡(x)w = \tan{\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:
w1=D−b2aw_{1} = \frac{\sqrt{D} - b}{2 a}
w2=−D−b2aw_{2} = \frac{- \sqrt{D} - b}{2 a}
donde D = b^2 - 4*a*c es el discriminante.
Como
a=1a = 1
b=0b = 0
c=−2c = -2
, entonces
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (-2) = 8

Como D > 0 la ecuación tiene dos raíces.
w1 = (-b + sqrt(D)) / (2*a)

w2 = (-b - sqrt(D)) / (2*a)

o
w1=2w_{1} = \sqrt{2}
w2=−2w_{2} = - \sqrt{2}
hacemos cambio inverso
tan⁡(x)=w\tan{\left(x \right)} = w
Tenemos la ecuación
tan⁡(x)=w\tan{\left(x \right)} = w
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
x=πn+atan⁡(w)x = \pi n + \operatorname{atan}{\left(w \right)}
O
x=πn+atan⁡(w)x = \pi n + \operatorname{atan}{\left(w \right)}
, donde n es cualquier número entero
sustituimos w:
x1=πn+atan⁡(w1)x_{1} = \pi n + \operatorname{atan}{\left(w_{1} \right)}
x1=πn+atan⁡(2)x_{1} = \pi n + \operatorname{atan}{\left(\sqrt{2} \right)}
x1=πn+atan⁡(2)x_{1} = \pi n + \operatorname{atan}{\left(\sqrt{2} \right)}
x2=πn+atan⁡(w2)x_{2} = \pi n + \operatorname{atan}{\left(w_{2} \right)}
x2=πn+atan⁡(−2)x_{2} = \pi n + \operatorname{atan}{\left(- \sqrt{2} \right)}
x2=πn−atan⁡(2)x_{2} = \pi n - \operatorname{atan}{\left(\sqrt{2} \right)}
Gráfica
0-80-60-40-2020406080-10010002000000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
          /  ___\
x1 = -atan\\/ 2 /
x1=−atan⁡(2)x_{1} = - \operatorname{atan}{\left(\sqrt{2} \right)} 
         /  ___\
x2 = atan\\/ 2 /
x2=atan⁡(2)x_{2} = \operatorname{atan}{\left(\sqrt{2} \right)} 
x2 = atan(sqrt(2))
Suma y producto de raíces [src] 
suma
      /  ___\       /  ___\
- atan\\/ 2 / + atan\\/ 2 /
−atan⁡(2)+atan⁡(2)- \operatorname{atan}{\left(\sqrt{2} \right)} + \operatorname{atan}{\left(\sqrt{2} \right)} 
=
0
00 
producto
     /  ___\     /  ___\
-atan\\/ 2 /*atan\\/ 2 /
−atan⁡(2)atan⁡(2)- \operatorname{atan}{\left(\sqrt{2} \right)} \operatorname{atan}{\left(\sqrt{2} \right)} 
=
     2/  ___\
-atan \\/ 2 /
−atan⁡2(2)- \operatorname{atan}^{2}{\left(\sqrt{2} \right)} 
-atan(sqrt(2))^2
Respuesta numérica [src] 
x1 = 70.0703549971
x2 = 68.1597217608509
x3 = 76.3535403042795
x4 = -85.7783182650489
x5 = 96.4340556431591
x6 = 17.8942393034142
x7 = -1315.372005236
x8 = 90.1508703359795
x9 = -55.5933511464918
x10 = 30.4606099177734
x11 = -83.8676850287999
x12 = 61.8765364536714
x13 = 38.654428461202
x14 = -24.1774246105938
x15 = 63.7871696899204
x16 = 82.6367256114591
x17 = 54.362391729151
x18 = 74.4429070680305
x19 = -41.7960211147918
x20 = -52.451758492902
x21 = 52.451758492902
x22 = -61.8765364536714
x23 = 8.46946134264487
x24 = -54.362391729151
x25 = -17.8942393034142
x26 = -27.3190172641836
x27 = 13.5216872324837
x28 = 98.3446888794081
x29 = 55.5933511464918
x30 = -30.4606099177734
x31 = 83.8676850287999
x32 = 60.6455770363306
x33 = -8.46946134264487
x34 = 1940.54894330037
x35 = 10.3800945788939
x36 = 11.6110539962347
x37 = -48.0792064219714
x38 = 46.1685731857224
x39 = -4.0969092717143
x40 = -90.1508703359795
x41 = -74.4429070680305
x42 = 0.955316618124509
x43 = -858.610111048138
x44 = 26.0880578468429
x45 = -99.5756482967489
x46 = -19.8048725396633
x47 = -13.5216872324837
x48 = 32.3712431540224
x49 = -26.0880578468429
x50 = -70.0703549971
x51 = 39.8853878785428
x52 = 24.1774246105938
x53 = -63.7871696899204
x54 = 19.8048725396633
x55 = -95440182.7104178
x56 = -77.5844997216203
x57 = -35.5128358076122
x58 = 33.6022025713632
x59 = -10.3800945788939
x60 = 65.0181291072611
x61 = -79.4951329578693
x62 = 85.7783182650489
x63 = -92.0615035722285
x64 = 2.18627603546528
x65 = 92.0615035722285
x66 = -46.1685731857224
x67 = 48.0792064219714
x68 = -32.3712431540224
x69 = -33.6022025713632
x70 = -96.4340556431591
x71 = 80.7260923752101
x72 = 41.7960211147918
x73 = -2.18627603546528
x74 = -76.3535403042795
x75 = -11.6110539962347
x76 = -68.1597217608509
x77 = 4.0969092717143
x78 = -87.0092776823897
x79 = -39.8853878785428
x80 = -16.6632798860735
x81 = -57.5039843827408
x81 = -57.5039843827408
    © Sr Examen – Калькулятор