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La ecuación:
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
Expresiones idénticas
6sin^2x+ tres cosxsinx-2cos^2x=3
6 seno de al cuadrado x más 3 coseno de x seno de x menos 2 coseno de al cuadrado x es igual a 3
6 seno de al cuadrado x más tres coseno de x seno de x menos 2 coseno de al cuadrado x es igual a 3
6sin2x+3cosxsinx-2cos2x=3
6sin²x+3cosxsinx-2cos²x=3
6sin en el grado 2x+3cosxsinx-2cos en el grado 2x=3
Expresiones semejantes
6sin^2x+3cosxsinx+2cos^2x=3
6sin^2x-3cosxsinx-2cos^2x=3

6sin^2x+3cosxsinx-2cos^2x=3 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

     2                             2       
6*sin (x) + 3*cos(x)*sin(x) - 2*cos (x) = 3

$$\left(6 \sin^{2}{\left(x \right)} + \sin{\left(x \right)} 3 \cos{\left(x \right)}\right) - 2 \cos^{2}{\left(x \right)} = 3$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

           /                         _______________\
           |         ____     ___   /          ____ |
           |  3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |
x1 = 2*atan|- -- + ------ + ------------------------|
           \  10     10                10           /

$$x_{1} = 2 \operatorname{atan}{\left(- \frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)}$$

            /                       _______________\
            |       ____     ___   /          ____ |
            |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |
x2 = -2*atan|-- + ------ + ------------------------|
            \10     10                10           /

$$x_{2} = - 2 \operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} \right)}$$

            /                       _______________\
            |       ____     ___   /          ____ |
            |3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |
x3 = -2*atan|-- - ------ + ------------------------|
            \10     10                10           /

$$x_{3} = - 2 \operatorname{atan}{\left(- \frac{\sqrt{69}}{10} + \frac{3}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)}$$

            /                       _______________\
            |       ____     ___   /          ____ |
            |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |
x4 = -2*atan|-- + ------ - ------------------------|
            \10     10                10           /

$$x_{4} = - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} + \frac{3}{10} + \frac{\sqrt{69}}{10} \right)}$$

x4 = -2*atan(-sqrt(2)*sqrt(3*sqrt(69) + 89)/10 + 3/10 + sqrt(69)/10)

Suma y producto de raíces [src]

suma

      /                         _______________\         /                       _______________\         /                       _______________\         /                       _______________\
      |         ____     ___   /          ____ |         |       ____     ___   /          ____ |         |       ____     ___   /          ____ |         |       ____     ___   /          ____ |
      |  3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |         |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |         |3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |         |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |
2*atan|- -- + ------ + ------------------------| - 2*atan|-- + ------ + ------------------------| - 2*atan|-- - ------ + ------------------------| - 2*atan|-- + ------ - ------------------------|
      \  10     10                10           /         \10     10                10           /         \10     10                10           /         \10     10                10           /

$$\left(- 2 \operatorname{atan}{\left(- \frac{\sqrt{69}}{10} + \frac{3}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)} + \left(- 2 \operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} \right)} + 2 \operatorname{atan}{\left(- \frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)}\right)\right) - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} + \frac{3}{10} + \frac{\sqrt{69}}{10} \right)}$$

        /                       _______________\         /                       _______________\         /                       _______________\         /                         _______________\
        |       ____     ___   /          ____ |         |       ____     ___   /          ____ |         |       ____     ___   /          ____ |         |         ____     ___   /          ____ |
        |3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |         |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |         |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |         |  3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |
- 2*atan|-- - ------ + ------------------------| - 2*atan|-- + ------ - ------------------------| - 2*atan|-- + ------ + ------------------------| + 2*atan|- -- + ------ + ------------------------|
        \10     10                10           /         \10     10                10           /         \10     10                10           /         \  10     10                10           /

$$- 2 \operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} \right)} - 2 \operatorname{atan}{\left(- \frac{\sqrt{69}}{10} + \frac{3}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)} - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} + \frac{3}{10} + \frac{\sqrt{69}}{10} \right)} + 2 \operatorname{atan}{\left(- \frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)}$$

producto

      /                         _______________\        /                       _______________\        /                       _______________\        /                       _______________\
      |         ____     ___   /          ____ |        |       ____     ___   /          ____ |        |       ____     ___   /          ____ |        |       ____     ___   /          ____ |
      |  3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |        |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |        |3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |        |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |
2*atan|- -- + ------ + ------------------------|*-2*atan|-- + ------ + ------------------------|*-2*atan|-- - ------ + ------------------------|*-2*atan|-- + ------ - ------------------------|
      \  10     10                10           /        \10     10                10           /        \10     10                10           /        \10     10                10           /

$$2 \operatorname{atan}{\left(- \frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)} \left(- 2 \operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} \right)}\right) \left(- 2 \operatorname{atan}{\left(- \frac{\sqrt{69}}{10} + \frac{3}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)}\right) \left(- 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} + \frac{3}{10} + \frac{\sqrt{69}}{10} \right)}\right)$$

        /                         _______________\     /                       _______________\     /                       _______________\     /                       _______________\
        |         ____     ___   /          ____ |     |       ____     ___   /          ____ |     |       ____     ___   /          ____ |     |       ____     ___   /          ____ |
        |  3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |     |3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |     |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |     |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |
-16*atan|- -- + ------ + ------------------------|*atan|-- - ------ + ------------------------|*atan|-- + ------ - ------------------------|*atan|-- + ------ + ------------------------|
        \  10     10                10           /     \10     10                10           /     \10     10                10           /     \10     10                10           /

$$- 16 \operatorname{atan}{\left(- \frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)} \operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} \right)} \operatorname{atan}{\left(- \frac{\sqrt{69}}{10} + \frac{3}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)} \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} + \frac{3}{10} + \frac{\sqrt{69}}{10} \right)}$$

-16*atan(-3/10 + sqrt(69)/10 + sqrt(2)*sqrt(89 - 3*sqrt(69))/10)*atan(3/10 - sqrt(69)/10 + sqrt(2)*sqrt(89 - 3*sqrt(69))/10)*atan(3/10 + sqrt(69)/10 - sqrt(2)*sqrt(89 + 3*sqrt(69))/10)*atan(3/10 + sqrt(69)/10 + sqrt(2)*sqrt(89 + 3*sqrt(69))/10)

Respuesta numérica [src]

x1 = 32.1400766289699

x2 = -982.594350480533

x3 = 22.7152986682005

x4 = -40.1165544035954

x5 = -79.6227371030873

x6 = 58.6073396548636

x7 = -98.4722930246261

x8 = -26.2156619920609

x9 = -24.4085911356464

x10 = -18.1254058284668

x11 = -77.8156662466729

x12 = 3.86574274666173

x13 = 8.34185719742687

x14 = -51.3484032207792

x15 = 60.414410511278

x16 = -68.3908882859035

x17 = 99.4480441515309

x18 = 33.4745984261452

x19 = -63.9147738351384

x20 = 96.3064514979411

x21 = -71.5324809394933

x22 = 16.4321133610209

x23 = -222.328928311803

x24 = -95.3307003710363

x25 = 38.4232619361495

x26 = -33.8333690964158

x27 = 25.8568913217903

x28 = -4.2245134169323

x29 = 0.724150093071939

x30 = 69.8391884720474

x31 = -90.3820368610321

x32 = -7.3661060705221

x33 = -27.5501837892362

x34 = 47.8480398969188

x35 = -10.5076987241119

x36 = -5.55903521410765

x37 = -41.9236252600098

x38 = 17.7666351581962

x39 = 91.8303370471759

x40 = 54.1312252040984

x41 = -49.5413323643648

x42 = 61.7489323084534

x43 = -46.399739710775

x44 = 2.05867189024728

x45 = 98.1135223543555

x46 = 66.6975958184576

x47 = -65.2492956323137

x48 = -21.2669984820566

x49 = 19.5737060146107

x50 = 44.706447243329

x51 = -29.3572546456506

x52 = 82.4055590864066

x53 = 36032.9848159116

x54 = -11.8422205212872

x55 = 2229.44786328541

x56 = 90.0232661907615

x57 = 88.6887443935861

x58 = -85.9059224102669

x59 = -55.8245176715443

x60 = -70.197959142318

x61 = -2.41744256051785

x62 = -35.6404399528302

x63 = 76.122373779227

x64 = -93.5236295146219

x65 = -48.2068105671894

x66 = 63.5560031648678

x67 = 11.4834498510167

x68 = -62.1077029787239

x69 = 24.0498204653758

x70 = 68.0321176156329

x71 = 130.863970687429

x72 = 36.616191079735

x73 = -87.2404442074423

x74 = -32.4988472992404

x75 = -84.0988515538525

x76 = -19.9324766848813

x77 = 30.3330057725554

x78 = 55.4657470012738

x79 = -54.489995874369

x80 = -73.3395517959078

x81 = -99.8068148218014

x82 = 39.7577837333248

x83 = 14.6250425046065

x84 = -43.2581470571852

x85 = 52.324154347684

x86 = -13.6492913777017

x87 = -57.6315885279588

x88 = 10.1489280538413

x89 = 80.5984882299921

x90 = -76.4811444494975

x91 = 74.3153029228125

x92 = -92.1891077174465

x93 = 46.0409690405044

x94 = 83.7400808835819

x95 = 41.5648545897392

x96 = 77.4568955764023

x96 = 77.4568955764023

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Expresiones idénticas

Expresiones semejantes

6sin^2x+3cosxsinx-2cos^2x=3 la ecuación

Solución numérica:

Solución