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- La ecuación:
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Ecuación x^2+5x=36
-
Ecuación 3*x=8
-
Ecuación 9-7(x+3)=5-6x
-
Ecuación 4x-5=3+2(x+1)
- Expresar {x} en función de y en la ecuación:
- -17*x+2*y=9
- 10*x-15*y=16
- -17*x+2*y=-4
- -2*x-19*y=3
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Expresiones idénticas
- dos cos^ dos (x)+ uno = dos sqrt(2)cos((3pi/2)-x)
- 2 coseno de al cuadrado (x) más 1 es igual a 2 raíz cuadrada de (2) coseno de ((3 número pi dividir por 2) menos x)
- dos coseno de en el grado dos (x) más uno es igual a dos raíz cuadrada de (2) coseno de ((3 número pi dividir por 2) menos x)
- 2cos^2(x)+1=2√(2)cos((3pi/2)-x)
- 2cos2(x)+1=2sqrt(2)cos((3pi/2)-x)
- 2cos2x+1=2sqrt2cos3pi/2-x
- 2cos²(x)+1=2sqrt(2)cos((3pi/2)-x)
- 2cos en el grado 2(x)+1=2sqrt(2)cos((3pi/2)-x)
- 2cos^2x+1=2sqrt2cos3pi/2-x
- 2cos^2(x)+1=2sqrt(2)cos((3pi dividir por 2)-x)
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Expresiones semejantes
- 2*(cos(x))^2+1=2*sqrt(2)*cos((3*pi/2)-x)
- 2cos^2(x)+1=2sqrt(2)cos((3pi/2)+x)
- 2cos^2(x)-1=2sqrt(2)cos((3pi/2)-x)
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Expresiones con funciones
- Coseno cos
- cos(2*x)+3*sin(x)+1=0
- cos(x)=4/7
- cos2x+5sinx+2=0
- cos(x)/(sin(x)-1)=0
- cos^2(x)-1=0
2cos^2(x)+1=2sqrt(2)cos((3pi/2)-x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 ___ /3*pi \
2*cos (x) + 1 = 2*\/ 2 *cos|---- - x|
\ 2 /
$$2 \cos^{2}{\left(x \right)} + 1 = 2 \sqrt{2} \cos{\left(- x + \frac{3 \pi}{2} \right)}$$
Respuesta rápida
[src]
-3*pi
x1 = -----
4
$$x_{1} = - \frac{3 \pi}{4}$$
-pi
x2 = ----
4
$$x_{2} = - \frac{\pi}{4}$$
/ / ___ ___\\ / / ___ ___\\
| |\/ 2 I*\/ 7 || | |\/ 2 I*\/ 7 ||
x3 = 2*re|atan|----- - -------|| + 2*I*im|atan|----- - -------||
\ \ 3 3 // \ \ 3 3 //
$$x_{3} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} - \frac{\sqrt{7} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} - \frac{\sqrt{7} i}{3} \right)}\right)}$$
/ / ___ ___\\ / / ___ ___\\
| |\/ 2 I*\/ 7 || | |\/ 2 I*\/ 7 ||
x4 = 2*re|atan|----- + -------|| + 2*I*im|atan|----- + -------||
\ \ 3 3 // \ \ 3 3 //
$$x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} + \frac{\sqrt{7} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} + \frac{\sqrt{7} i}{3} \right)}\right)}$$
x4 = 2*re(atan(sqrt(2)/3 + sqrt(7)*i/3)) + 2*i*im(atan(sqrt(2)/3 + sqrt(7)*i/3))
Suma y producto de raíces
[src]
suma
/ / ___ ___\\ / / ___ ___\\ / / ___ ___\\ / / ___ ___\\ 3*pi pi | |\/ 2 I*\/ 7 || | |\/ 2 I*\/ 7 || | |\/ 2 I*\/ 7 || | |\/ 2 I*\/ 7 || - ---- - -- + 2*re|atan|----- - -------|| + 2*I*im|atan|----- - -------|| + 2*re|atan|----- + -------|| + 2*I*im|atan|----- + -------|| 4 4 \ \ 3 3 // \ \ 3 3 // \ \ 3 3 // \ \ 3 3 //
$$\left(\left(- \frac{3 \pi}{4} - \frac{\pi}{4}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} - \frac{\sqrt{7} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} - \frac{\sqrt{7} i}{3} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} + \frac{\sqrt{7} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} + \frac{\sqrt{7} i}{3} \right)}\right)}\right)$$
=
/ / ___ ___\\ / / ___ ___\\ / / ___ ___\\ / / ___ ___\\
| |\/ 2 I*\/ 7 || | |\/ 2 I*\/ 7 || | |\/ 2 I*\/ 7 || | |\/ 2 I*\/ 7 ||
-pi + 2*re|atan|----- - -------|| + 2*re|atan|----- + -------|| + 2*I*im|atan|----- - -------|| + 2*I*im|atan|----- + -------||
\ \ 3 3 // \ \ 3 3 // \ \ 3 3 // \ \ 3 3 //
$$- \pi + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} - \frac{\sqrt{7} i}{3} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} + \frac{\sqrt{7} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} - \frac{\sqrt{7} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} + \frac{\sqrt{7} i}{3} \right)}\right)}$$
producto
/ / / ___ ___\\ / / ___ ___\\\ / / / ___ ___\\ / / ___ ___\\\ -3*pi -pi | | |\/ 2 I*\/ 7 || | |\/ 2 I*\/ 7 ||| | | |\/ 2 I*\/ 7 || | |\/ 2 I*\/ 7 ||| -----*----*|2*re|atan|----- - -------|| + 2*I*im|atan|----- - -------|||*|2*re|atan|----- + -------|| + 2*I*im|atan|----- + -------||| 4 4 \ \ \ 3 3 // \ \ 3 3 /// \ \ \ 3 3 // \ \ 3 3 ///
$$- \frac{3 \pi}{4} \left(- \frac{\pi}{4}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} - \frac{\sqrt{7} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} - \frac{\sqrt{7} i}{3} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} + \frac{\sqrt{7} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} + \frac{\sqrt{7} i}{3} \right)}\right)}\right)$$
=
/ / / ___ ___\\ / / ___ ___\\\ / / / ___ ___\\ / / ___ ___\\\
2 | | |\/ 2 I*\/ 7 || | |\/ 2 I*\/ 7 ||| | | |\/ 2 I*\/ 7 || | |\/ 2 I*\/ 7 |||
3*pi *|I*im|atan|----- - -------|| + re|atan|----- - -------|||*|I*im|atan|----- + -------|| + re|atan|----- + -------|||
\ \ \ 3 3 // \ \ 3 3 /// \ \ \ 3 3 // \ \ 3 3 ///
-------------------------------------------------------------------------------------------------------------------------
4
$$\frac{3 \pi^{2} \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} - \frac{\sqrt{7} i}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} - \frac{\sqrt{7} i}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} + \frac{\sqrt{7} i}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2}}{3} + \frac{\sqrt{7} i}{3} \right)}\right)}\right)}{4}$$
3*pi^2*(i*im(atan(sqrt(2)/3 - i*sqrt(7)/3)) + re(atan(sqrt(2)/3 - i*sqrt(7)/3)))*(i*im(atan(sqrt(2)/3 + i*sqrt(7)/3)) + re(atan(sqrt(2)/3 + i*sqrt(7)/3)))/4
Respuesta numérica
[src]
x1 = -88.7499924639117
x2 = 93.4623814442964
x3 = 30.6305283725005
x4 = 55.7632696012188
x5 = -84.037603483527
x6 = 22.776546738526
x7 = 3.92699081698724
x8 = -96.6039740978861
x9 = -33.7721210260903
x10 = 10.2101761241668
x11 = -25.9181393921158
x12 = 16.4933614313464
x13 = -849.015414632642
x14 = 49.4800842940392
x15 = -76.1836218495525
x16 = -21.2057504117311
x17 = 47.9092879672443
x18 = 29.0597320457056
x19 = 99.7455667514759
x20 = 60.4756585816035
x21 = 85.6083998103219
x22 = 74.6128255227576
x23 = 62.0464549083984
x24 = -57.3340659280137
x25 = -0.785398163397448
x26 = 43.1968989868597
x27 = -2.35619449019234
x28 = -126.449104306989
x29 = -65.1880475619882
x30 = -14.9225651045515
x31 = -69.9004365423729
x32 = -51.0508806208341
x33 = 68.329640215578
x34 = 18.0641577581413
x35 = 87.1791961371168
x36 = 54.1924732744239
x37 = -40.0553063332699
x38 = -63.6172512351933
x39 = 5.49778714378214
x40 = 11.7809724509617
x41 = 98.174770424681
x42 = 41.6261026600648
x43 = -82.4668071567321
x44 = -58.9048622548086
x45 = -19.6349540849362
x46 = -101.316363078271
x47 = -44.7676953136546
x48 = -46.3384916404494
x49 = -77.7544181763474
x50 = 24.3473430653209
x51 = -32.2013246992954
x52 = -52.621676947629
x53 = -90.3207887907066
x54 = -13.3517687777566
x55 = -27.4889357189107
x56 = 91.8915851175014
x57 = 73.0420291959627
x58 = -38.484510006475
x59 = 66.7588438887831
x60 = -71.4712328691678
x60 = -71.4712328691678