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- La ecuación:
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Ecuación 7x^2+21x=0
-
Ecuación x^4-x^2-12=0
- Ecuación (x-2)²+(x+1)²-(x-5)(x+5)=45
- Ecuación 3x^2-4x+1/2x^2-4x
- Expresar {x} en función de y en la ecuación:
- 15*x+14*y=19
- 14*x-16*y=-3
- -10*x-15*y=9
- 9*x-8*y=6
- Integral de d{x}:
- ctg²x
-
Expresiones idénticas
- ctg²x= uno
- ctg²x es igual a 1
- ctg²x es igual a uno
ctg²x=1 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\cot^{2}{\left(x \right)} = 1$$
cambiamos
$$\cot^{2}{\left(x \right)} - 1 = 0$$
$$\cot^{2}{\left(x \right)} - 1 = 0$$
Sustituimos
$$w = \cot{\left(x \right)}$$
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
$$a = 1$$
$$b = 0$$
$$c = -1$$
, entonces
Como D > 0 la ecuación tiene dos raíces.
o
$$w_{1} = 1$$
$$w_{2} = -1$$
hacemos cambio inverso
$$\cot{\left(x \right)} = w$$
sustituimos w:
$$\cot^{2}{\left(x \right)} = 1$$
cambiamos
$$\cot^{2}{\left(x \right)} - 1 = 0$$
$$\cot^{2}{\left(x \right)} - 1 = 0$$
Sustituimos
$$w = \cot{\left(x \right)}$$
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
$$a = 1$$
$$b = 0$$
$$c = -1$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-1) = 4
Como D > 0 la ecuación tiene dos raíces.
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
o
$$w_{1} = 1$$
$$w_{2} = -1$$
hacemos cambio inverso
$$\cot{\left(x \right)} = w$$
sustituimos w:
Suma y producto de raíces
[src]
suma
pi pi - -- + -- 4 4
$$- \frac{\pi}{4} + \frac{\pi}{4}$$
=
0
$$0$$
producto
-pi pi ----*-- 4 4
$$- \frac{\pi}{4} \frac{\pi}{4}$$
=
2 -pi ----- 16
$$- \frac{\pi^{2}}{16}$$
-pi^2/16
Respuesta rápida
[src]
-pi
x1 = ----
4
$$x_{1} = - \frac{\pi}{4}$$
pi
x2 = --
4
$$x_{2} = \frac{\pi}{4}$$
x2 = pi/4
Respuesta numérica
[src]
x1 = 99.7455667514759
x2 = -25.9181393921158
x3 = -38.484510006475
x4 = -84.037603483527
x5 = 96.6039740978861
x6 = -55.7632696012188
x7 = -71.4712328691678
x8 = -190.85175370558
x9 = -79.3252145031423
x10 = 57.3340659280137
x11 = -52.621676947629
x12 = 49.4800842940392
x13 = 5.49778714378214
x14 = -87.1791961371168
x15 = -21.2057504117311
x16 = 82.4668071567321
x17 = -11.7809724509617
x18 = 60.4756585816035
x19 = -35.3429173528852
x20 = 38.484510006475
x21 = 44.7676953136546
x22 = 76.1836218495525
x23 = -10.2101761241668
x24 = -77.7544181763474
x25 = -101.316363078271
x26 = 16.4933614313464
x27 = 69.9004365423729
x28 = 32.2013246992954
x29 = 74.6128255227576
x30 = 68.329640215578
x31 = -16.4933614313464
x32 = 71.4712328691678
x33 = -85.6083998103219
x34 = 22.776546738526
x35 = 11.7809724509617
x36 = -3.92699081698724
x37 = 90.3207887907066
x38 = -82.4668071567321
x39 = -41.6261026600648
x40 = -27.4889357189107
x41 = -18.0641577581413
x42 = -62.0464549083984
x43 = -19.6349540849362
x44 = -47.9092879672443
x45 = -32.2013246992954
x46 = 24.3473430653209
x47 = -49.4800842940392
x48 = -93.4623814442964
x49 = 47.9092879672443
x50 = -65.1880475619882
x51 = -43.1968989868597
x52 = 8.63937979737193
x53 = 77.7544181763474
x54 = 54.1924732744239
x55 = -98.174770424681
x56 = 27.4889357189107
x57 = -13.3517687777566
x58 = 55.7632696012188
x59 = -76.1836218495525
x60 = -5.49778714378214
x61 = -68.329640215578
x62 = -60.4756585816035
x63 = 84.037603483527
x64 = 3.92699081698724
x65 = 10.2101761241668
x66 = 219.126087587888
x67 = -69.9004365423729
x68 = 52.621676947629
x69 = -33.7721210260903
x70 = 66.7588438887831
x71 = -54.1924732744239
x72 = -168.860605130451
x73 = 33.7721210260903
x74 = 46.3384916404494
x75 = -63.6172512351933
x76 = -91.8915851175014
x77 = 2.35619449019234
x78 = 88.7499924639117
x79 = 25.9181393921158
x80 = 40.0553063332699
x81 = 91.8915851175014
x82 = -90.3207887907066
x83 = 93.4623814442964
x84 = 30.6305283725005
x85 = -40.0553063332699
x86 = 98.174770424681
x87 = 18.0641577581413
x88 = 62.0464549083984
x89 = -99.7455667514759
x90 = -57.3340659280137
x90 = -57.3340659280137