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- La ecuación:
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Ecuación 3^x+4^x=5^x
-
Ecuación (x-2)^4+3*(x-2)^2-10=0
-
Ecuación x+2/x=3
-
Ecuación x^2=-2
- Expresar {x} en función de y en la ecuación:
- 15*x+10*y=-4
- -9*x-15*y=-4
- -13*x+7*y=11
- -7*x-7*y=-14
-
Expresiones idénticas
- cos4x- uno : dos = cero
- coseno de 4x menos 1:2 es igual a 0
- coseno de 4x menos uno : dos es igual a cero
- cos4x-1:2=O
-
Expresiones semejantes
- cos4x+1:2=0
cos4x-1:2=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\cos{\left(4 x \right)} - \frac{1}{2} = 0$$
es la ecuación trigonométrica más simple
Obtenemos:
$$\cos{\left(4 x \right)} = \frac{1}{2}$$
Esta ecuación se reorganiza en
$$4 x = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$4 x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
O
$$4 x = \pi n + \frac{\pi}{3}$$
$$4 x = \pi n - \frac{2 \pi}{3}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$4$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{4} + \frac{\pi}{12}$$
$$x_{2} = \frac{\pi n}{4} - \frac{\pi}{6}$$
$$\cos{\left(4 x \right)} - \frac{1}{2} = 0$$
es la ecuación trigonométrica más simple
Transportemos -1/2 al miembro derecho de la ecuación
cambiando el signo de -1/2
Obtenemos:
$$\cos{\left(4 x \right)} = \frac{1}{2}$$
Esta ecuación se reorganiza en
$$4 x = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$4 x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
O
$$4 x = \pi n + \frac{\pi}{3}$$
$$4 x = \pi n - \frac{2 \pi}{3}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$4$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{4} + \frac{\pi}{12}$$
$$x_{2} = \frac{\pi n}{4} - \frac{\pi}{6}$$
Suma y producto de raíces
[src]
suma
pi 5*pi -- + ---- 12 12
$$\frac{\pi}{12} + \frac{5 \pi}{12}$$
=
pi -- 2
$$\frac{\pi}{2}$$
producto
pi 5*pi --*---- 12 12
$$\frac{\pi}{12} \frac{5 \pi}{12}$$
=
2 5*pi ----- 144
$$\frac{5 \pi^{2}}{144}$$
5*pi^2/144
Respuesta rápida
[src]
pi
x1 = --
12
$$x_{1} = \frac{\pi}{12}$$
5*pi
x2 = ----
12
$$x_{2} = \frac{5 \pi}{12}$$
x2 = 5*pi/12
Respuesta numérica
[src]
x1 = 9.16297857297023
x2 = 62.5700536839967
x3 = 12.30457122656
x4 = 1448.53601269269
x5 = -81.9432083811338
x6 = -31.6777259236971
x7 = -65.7116463375865
x8 = 0.261799387799149
x9 = -53.6688744988256
x10 = 8.11578102177363
x11 = -89.7971900151083
x12 = -75.6600230739542
x13 = -100.269165527074
x14 = 78.2780169519457
x15 = -61.5228561328001
x16 = 22.2529479629277
x17 = 468.359104772678
x18 = 1.83259571459405
x19 = 6.02138591938044
x20 = -93.9859802198946
x21 = 93.9859802198946
x22 = -15.9697626557481
x23 = -39.5317075576716
x24 = -42.1497014356631
x25 = -97.6511716490827
x26 = 52.0980781720307
x27 = -79.8488132787406
x28 = 100.269165527074
x29 = -57.857664703612
x30 = -23.8237442897226
x31 = -45.2912940892529
x32 = -21.7293491873294
x33 = 66.2352451131848
x34 = -71.9948316447661
x35 = -67.8060414399797
x36 = -6.02138591938044
x37 = 37.9609112308767
x38 = 88.2263936883134
x39 = 15.9697626557481
x40 = 23.8237442897226
x41 = 34.2957198016886
x42 = 86.1319985859202
x43 = -59.9520598060052
x44 = 92.9387826686981
x45 = 71.9948316447661
x46 = -96.0803753222878
x47 = -28.012534494509
x48 = -37.9609112308767
x49 = 70.4240353179712
x50 = -86.1319985859202
x51 = -12.8281700021583
x52 = -87.7027949127151
x53 = -30.1069295969022
x54 = 20.1585528605345
x55 = 85.0848010347236
x56 = -43.720497762458
x57 = 44.2440965380563
x58 = 42.1497014356631
x59 = 89.7971900151083
x60 = -83.5140047079287
x61 = -17.540558982543
x62 = -74.0892267471593
x63 = -52.0980781720307
x64 = -45.8148928648512
x65 = -20.1585528605345
x66 = 87.7027949127151
x67 = 96.0803753222878
x68 = 45.8148928648512
x69 = 26.4417381677141
x70 = -35.8665161284835
x71 = 92.4151838930998
x72 = -34.8193185772869
x73 = 56.2868683768171
x74 = 67.8060414399797
x75 = -64.6644487863899
x76 = -1.83259571459405
x77 = 74.0892267471593
x78 = 64.1408500107916
x79 = -9.68657734856853
x80 = 50.0036830696375
x81 = 81.9432083811338
x82 = 4.45058959258554
x83 = 48.4328867428426
x84 = 28.012534494509
x85 = 59.9520598060052
x86 = 126.972703082587
x87 = 30.1069295969022
x88 = -64.1408500107916
x89 = -13.8753675533549
x90 = -78.2780169519457
x91 = -50.0036830696375
x91 = -50.0036830696375