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La ecuación:
Ecuación 2*x^2+6*x+9=0
Ecuación cos(x)=2
Ecuación sqrt(x^2-x-1)-sqrt(x)=1
Ecuación sin(x/4)=1/2
Expresar {x} en función de y en la ecuación:
10*x+5*y=-17
16*x-17*y=-9
-10*x+16*y=-6
7*x+13*y=-13
Expresiones idénticas
sinx*cosx-2cosx= cero
seno de x multiplicar por coseno de x menos 2 coseno de x es igual a 0
seno de x multiplicar por coseno de x menos 2 coseno de x es igual a cero
sinxcosx-2cosx=0
sinx*cosx-2cosx=O
Expresiones semejantes
sin(x)^(2)-sin(x)*cos(x)-2*cos(x)^(2)=0
3*sin(x)^2-sin(x)cos(x)-2*cos(x)^2=0
3*sin(x)*sin(x)+sin(x)*cos(x)-2*cos(x)*cos(x)=0
sinx*cosx+2cosx=0
Expresiones con funciones
sinx
sinx-cosx=0
sinx=1/2
sinx=1/4
sinx=-√2
sinx(2sinx-1)=0
cosx
cosx=√3÷2
cosx-2cos(3x)+cos(5x)=0
cosx/9=-1
cosx=1
cosx=-√2/2

sinx*cosx-2cosx=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

sin(x)*cos(x) - 2*cos(x) = 0

$$\sin{\left(x \right)} \cos{\left(x \right)} - 2 \cos{\left(x \right)} = 0$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

                /    /        ___\\         /    /        ___\\       /    /        ___\\         /    /        ___\\
  pi   pi       |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
- -- + -- + 2*re|atan|- - -------|| + 2*I*im|atan|- - -------|| + 2*re|atan|- + -------|| + 2*I*im|atan|- + -------||
  2    2        \    \2      2   //         \    \2      2   //       \    \2      2   //         \    \2      2   //

$$\left(\left(- \frac{\pi}{2} + \frac{\pi}{2}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)$$

    /    /        ___\\       /    /        ___\\         /    /        ___\\         /    /        ___\\
    |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
2*re|atan|- + -------|| + 2*re|atan|- - -------|| + 2*I*im|atan|- + -------|| + 2*I*im|atan|- - -------||
    \    \2      2   //       \    \2      2   //         \    \2      2   //         \    \2      2   //

$$2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}$$

producto

        /    /    /        ___\\         /    /        ___\\\ /    /    /        ___\\         /    /        ___\\\
-pi  pi |    |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||| |    |    |1   I*\/ 3 ||         |    |1   I*\/ 3 |||
----*--*|2*re|atan|- - -------|| + 2*I*im|atan|- - -------|||*|2*re|atan|- + -------|| + 2*I*im|atan|- + -------|||
 2   2  \    \    \2      2   //         \    \2      2   /// \    \    \2      2   //         \    \2      2   ///

$$- \frac{\pi}{2} \frac{\pi}{2} \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)$$

     /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\
   2 |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 ||| |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 |||
-pi *|I*im|atan|- + -------|| + re|atan|- + -------|||*|I*im|atan|- - -------|| + re|atan|- - -------|||
     \    \    \2      2   //     \    \2      2   /// \    \    \2      2   //     \    \2      2   ///

$$- \pi^{2} \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)$$

-pi^2*(i*im(atan(1/2 + i*sqrt(3)/2)) + re(atan(1/2 + i*sqrt(3)/2)))*(i*im(atan(1/2 - i*sqrt(3)/2)) + re(atan(1/2 - i*sqrt(3)/2)))

Respuesta rápida [src]

     -pi 
x1 = ----
      2

$$x_{1} = - \frac{\pi}{2}$$

     pi
x2 = --
     2

$$x_{2} = \frac{\pi}{2}$$

         /    /        ___\\         /    /        ___\\
         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
x3 = 2*re|atan|- - -------|| + 2*I*im|atan|- - -------||
         \    \2      2   //         \    \2      2   //

$$x_{3} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}$$

         /    /        ___\\         /    /        ___\\
         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
x4 = 2*re|atan|- + -------|| + 2*I*im|atan|- + -------||
         \    \2      2   //         \    \2      2   //

$$x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}$$

x4 = 2*re(atan(1/2 + sqrt(3)*i/2)) + 2*i*im(atan(1/2 + sqrt(3)*i/2))

Respuesta numérica [src]

x1 = 48.6946861306418

x2 = 54.9778714378214

x3 = -98.9601685880785

x4 = 67.5442420521806

x5 = 76.9690200129499

x6 = 36.1283155162826

x7 = 58.1194640914112

x8 = 14.1371669411541

x9 = -29.845130209103

x10 = 365.995544143211

x11 = 61.261056745001

x12 = -36.1283155162826

x13 = -4.71238898038469

x14 = -39.2699081698724

x15 = 1.5707963267949

x16 = -14.1371669411541

x17 = -64.4026493985908

x18 = -67.5442420521806

x19 = 92.6769832808989

x20 = -51.8362787842316

x21 = -86.3937979737193

x22 = 42.4115008234622

x23 = -17.2787595947439

x24 = -45.553093477052

x25 = -89.5353906273091

x26 = -1.5707963267949

x27 = 39.2699081698724

x28 = 23.5619449019235

x29 = 7.85398163397448

x30 = -58.1194640914112

x31 = -61.261056745001

x32 = -73.8274273593601

x33 = 73.8274273593601

x34 = 29.845130209103

x35 = 4.71238898038469

x36 = 86.3937979737193

x37 = 64.4026493985908

x38 = 89.5353906273091

x39 = -20.4203522483337

x40 = -26.7035375555132

x41 = 98.9601685880785

x42 = -1452.98660228528

x43 = 51.8362787842316

x44 = 83.2522053201295

x45 = -48.6946861306418

x46 = -54.9778714378214

x47 = 70.6858347057703

x48 = -95.8185759344887

x49 = 26.7035375555132

x50 = 80.1106126665397

x51 = -23.5619449019235

x52 = -7.85398163397448

x53 = -83.2522053201295

x54 = -76.9690200129499

x55 = -42.4115008234622

x56 = -32.9867228626928

x57 = -142.942465738336

x58 = 17.2787595947439

x59 = 32.9867228626928

x60 = 20.4203522483337

x61 = -70.6858347057703

x62 = -10.9955742875643

x63 = -92.6769832808989

x64 = 45.553093477052

x65 = 10.9955742875643

x66 = -80.1106126665397

x67 = 95.8185759344887

x67 = 95.8185759344887

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Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

sinx*cosx-2cosx=0 la ecuación

Solución numérica:

Solución