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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
2sin²x+3sinxcosx-8cos²x
2 seno de ²x más 3 seno de x coseno de x menos 8 coseno de ²x
Expresiones semejantes
2sin²x+3sinxcosx+8cos²x
2sin²x-3sinxcosx-8cos²x

2sin²x+3sinxcosx-8cos²x la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

     2                             2       
2*sin (x) + 3*sin(x)*cos(x) - 8*cos (x) = 0

$$\left(2 \sin^{2}{\left(x \right)} + 3 \sin{\left(x \right)} \cos{\left(x \right)}\right) - 8 \cos^{2}{\left(x \right)} = 0$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

      /                         ________________\         /                       ________________\         /                       ________________\         /                       ________________\
      |         ____     ___   /           ____ |         |       ____     ___   /           ____ |         |       ____     ___   /           ____ |         |       ____     ___   /           ____ |
      |  3    \/ 73    \/ 2 *\/  169 - 3*\/ 73  |         |3    \/ 73    \/ 2 *\/  169 + 3*\/ 73  |         |3    \/ 73    \/ 2 *\/  169 - 3*\/ 73  |         |3    \/ 73    \/ 2 *\/  169 + 3*\/ 73  |
2*atan|- -- + ------ + -------------------------| - 2*atan|-- + ------ + -------------------------| - 2*atan|-- - ------ + -------------------------| - 2*atan|-- + ------ - -------------------------|
      \  16     16                 16           /         \16     16                 16           /         \16     16                 16           /         \16     16                 16           /

$$\left(- 2 \operatorname{atan}{\left(- \frac{\sqrt{73}}{16} + \frac{3}{16} + \frac{\sqrt{2} \sqrt{169 - 3 \sqrt{73}}}{16} \right)} + \left(- 2 \operatorname{atan}{\left(\frac{3}{16} + \frac{\sqrt{73}}{16} + \frac{\sqrt{2} \sqrt{3 \sqrt{73} + 169}}{16} \right)} + 2 \operatorname{atan}{\left(- \frac{3}{16} + \frac{\sqrt{73}}{16} + \frac{\sqrt{2} \sqrt{169 - 3 \sqrt{73}}}{16} \right)}\right)\right) - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{73} + 169}}{16} + \frac{3}{16} + \frac{\sqrt{73}}{16} \right)}$$

        /                       ________________\         /                       ________________\         /                       ________________\         /                         ________________\
        |       ____     ___   /           ____ |         |       ____     ___   /           ____ |         |       ____     ___   /           ____ |         |         ____     ___   /           ____ |
        |3    \/ 73    \/ 2 *\/  169 - 3*\/ 73  |         |3    \/ 73    \/ 2 *\/  169 + 3*\/ 73  |         |3    \/ 73    \/ 2 *\/  169 + 3*\/ 73  |         |  3    \/ 73    \/ 2 *\/  169 - 3*\/ 73  |
- 2*atan|-- - ------ + -------------------------| - 2*atan|-- + ------ - -------------------------| - 2*atan|-- + ------ + -------------------------| + 2*atan|- -- + ------ + -------------------------|
        \16     16                 16           /         \16     16                 16           /         \16     16                 16           /         \  16     16                 16           /

$$- 2 \operatorname{atan}{\left(\frac{3}{16} + \frac{\sqrt{73}}{16} + \frac{\sqrt{2} \sqrt{3 \sqrt{73} + 169}}{16} \right)} - 2 \operatorname{atan}{\left(- \frac{\sqrt{73}}{16} + \frac{3}{16} + \frac{\sqrt{2} \sqrt{169 - 3 \sqrt{73}}}{16} \right)} - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{73} + 169}}{16} + \frac{3}{16} + \frac{\sqrt{73}}{16} \right)} + 2 \operatorname{atan}{\left(- \frac{3}{16} + \frac{\sqrt{73}}{16} + \frac{\sqrt{2} \sqrt{169 - 3 \sqrt{73}}}{16} \right)}$$

producto

      /                         ________________\        /                       ________________\        /                       ________________\        /                       ________________\
      |         ____     ___   /           ____ |        |       ____     ___   /           ____ |        |       ____     ___   /           ____ |        |       ____     ___   /           ____ |
      |  3    \/ 73    \/ 2 *\/  169 - 3*\/ 73  |        |3    \/ 73    \/ 2 *\/  169 + 3*\/ 73  |        |3    \/ 73    \/ 2 *\/  169 - 3*\/ 73  |        |3    \/ 73    \/ 2 *\/  169 + 3*\/ 73  |
2*atan|- -- + ------ + -------------------------|*-2*atan|-- + ------ + -------------------------|*-2*atan|-- - ------ + -------------------------|*-2*atan|-- + ------ - -------------------------|
      \  16     16                 16           /        \16     16                 16           /        \16     16                 16           /        \16     16                 16           /

$$2 \operatorname{atan}{\left(- \frac{3}{16} + \frac{\sqrt{73}}{16} + \frac{\sqrt{2} \sqrt{169 - 3 \sqrt{73}}}{16} \right)} \left(- 2 \operatorname{atan}{\left(\frac{3}{16} + \frac{\sqrt{73}}{16} + \frac{\sqrt{2} \sqrt{3 \sqrt{73} + 169}}{16} \right)}\right) \left(- 2 \operatorname{atan}{\left(- \frac{\sqrt{73}}{16} + \frac{3}{16} + \frac{\sqrt{2} \sqrt{169 - 3 \sqrt{73}}}{16} \right)}\right) \left(- 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{73} + 169}}{16} + \frac{3}{16} + \frac{\sqrt{73}}{16} \right)}\right)$$

        /                         ________________\     /                       ________________\     /                       ________________\     /                       ________________\
        |         ____     ___   /           ____ |     |       ____     ___   /           ____ |     |       ____     ___   /           ____ |     |       ____     ___   /           ____ |
        |  3    \/ 73    \/ 2 *\/  169 - 3*\/ 73  |     |3    \/ 73    \/ 2 *\/  169 - 3*\/ 73  |     |3    \/ 73    \/ 2 *\/  169 + 3*\/ 73  |     |3    \/ 73    \/ 2 *\/  169 + 3*\/ 73  |
-16*atan|- -- + ------ + -------------------------|*atan|-- - ------ + -------------------------|*atan|-- + ------ - -------------------------|*atan|-- + ------ + -------------------------|
        \  16     16                 16           /     \16     16                 16           /     \16     16                 16           /     \16     16                 16           /

$$- 16 \operatorname{atan}{\left(- \frac{3}{16} + \frac{\sqrt{73}}{16} + \frac{\sqrt{2} \sqrt{169 - 3 \sqrt{73}}}{16} \right)} \operatorname{atan}{\left(\frac{3}{16} + \frac{\sqrt{73}}{16} + \frac{\sqrt{2} \sqrt{3 \sqrt{73} + 169}}{16} \right)} \operatorname{atan}{\left(- \frac{\sqrt{73}}{16} + \frac{3}{16} + \frac{\sqrt{2} \sqrt{169 - 3 \sqrt{73}}}{16} \right)} \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{73} + 169}}{16} + \frac{3}{16} + \frac{\sqrt{73}}{16} \right)}$$

-16*atan(-3/16 + sqrt(73)/16 + sqrt(2)*sqrt(169 - 3*sqrt(73))/16)*atan(3/16 - sqrt(73)/16 + sqrt(2)*sqrt(169 - 3*sqrt(73))/16)*atan(3/16 + sqrt(73)/16 - sqrt(2)*sqrt(169 + 3*sqrt(73))/16)*atan(3/16 + sqrt(73)/16 + sqrt(2)*sqrt(169 + 3*sqrt(73))/16)

Respuesta rápida [src]

           /                         ________________\
           |         ____     ___   /           ____ |
           |  3    \/ 73    \/ 2 *\/  169 - 3*\/ 73  |
x1 = 2*atan|- -- + ------ + -------------------------|
           \  16     16                 16           /

$$x_{1} = 2 \operatorname{atan}{\left(- \frac{3}{16} + \frac{\sqrt{73}}{16} + \frac{\sqrt{2} \sqrt{169 - 3 \sqrt{73}}}{16} \right)}$$

            /                       ________________\
            |       ____     ___   /           ____ |
            |3    \/ 73    \/ 2 *\/  169 + 3*\/ 73  |
x2 = -2*atan|-- + ------ + -------------------------|
            \16     16                 16           /

$$x_{2} = - 2 \operatorname{atan}{\left(\frac{3}{16} + \frac{\sqrt{73}}{16} + \frac{\sqrt{2} \sqrt{3 \sqrt{73} + 169}}{16} \right)}$$

            /                       ________________\
            |       ____     ___   /           ____ |
            |3    \/ 73    \/ 2 *\/  169 - 3*\/ 73  |
x3 = -2*atan|-- - ------ + -------------------------|
            \16     16                 16           /

$$x_{3} = - 2 \operatorname{atan}{\left(- \frac{\sqrt{73}}{16} + \frac{3}{16} + \frac{\sqrt{2} \sqrt{169 - 3 \sqrt{73}}}{16} \right)}$$

            /                       ________________\
            |       ____     ___   /           ____ |
            |3    \/ 73    \/ 2 *\/  169 + 3*\/ 73  |
x4 = -2*atan|-- + ------ - -------------------------|
            \16     16                 16           /

$$x_{4} = - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{73} + 169}}{16} + \frac{3}{16} + \frac{\sqrt{73}}{16} \right)}$$

x4 = -2*atan(-sqrt(2)*sqrt(3*sqrt(73) + 169)/16 + 3/16 + sqrt(73)/16)

Respuesta numérica [src]

x1 = -89.2018370353616

x2 = -71.3108450921957

x3 = -7.52042804202701

x4 = -73.4938737674127

x5 = 66.9192316657552

x6 = 82.6271949337042

x7 = 98.3351582016531

x8 = -35.7947619243351

x9 = -11.6205846739896

x10 = -13.8036133492066

x11 = 32.3617124762675

x12 = -48.3611325386943

x13 = -4.37883538843722

x14 = -33.6117332491182

x15 = 36.4618691082301

x16 = -93.3019936673242

x17 = -95.4850223425412

x18 = -17.9037699811692

x19 = -42.0779472315147

x20 = 89.8689442192566

x21 = 88.9103802408838

x22 = 41.7864904370369

x23 = -27.3285479419386

x24 = 1.90434991874237

x25 = -32.6531692707454

x26 = -99.5851789745038

x27 = 58.4530176833586

x28 = 52.1698323761791

x29 = 83.585758912077

x30 = -68.1692524386059

x31 = 10.3705639011389

x32 = 85.768787587294

x33 = -92.3434296889514

x34 = 8.18753522592196

x35 = 44.9280830906267

x36 = 92.0519728944736

x37 = -24.1869552883488

x38 = -77.5940303993753

x39 = -46.1781038634773

x40 = 74.1609809513076

x41 = 63.7776390121654

x42 = -5.33739936681003

x43 = 0.945785940369558

x44 = -61.8860671314263

x45 = 60.6360463585756

x46 = 67.877795644128

x47 = -86.0602443817718

x48 = 80.4441662584872

x49 = 26.0785271690879

x50 = 33.3202764546403

x51 = -83.8772157065549

x52 = -90.1604010137344

x53 = 70.060824319345

x54 = -20.0867986563862

x55 = -79.7770590745923

x56 = 48.0696757442165

x57 = -29.5115766171556

x58 = 19.7953418619083

x59 = 55.3114250297689

x60 = -10.6620206956168

x61 = -51.5027251922841

x62 = -64.0690958066433

x63 = 132.892677391141

x64 = 39.6034617618199

x65 = 30.1786838010505

x66 = 17.6123131866913

x67 = 45.8866470689995

x68 = -39.8949185562978

x69 = 76.3440096265246

x70 = 139.17586269832

x71 = -70.3522811138229

x72 = 54.352861051396

x73 = 96.1521295264362

x74 = 14.4707205331015

x75 = 38.6448977834471

x76 = -26.3699839635658

x77 = -49.3196965170671

x78 = 23.8954984938709

x79 = -55.6028818242467

x80 = 77.3025736048974

x81 = 11.3291278795117

x82 = -54.6443178458739

x83 = 22.9369345154981

x84 = 16.6537492083185

x85 = -98.626614996131

x86 = -2.19580671322024

x87 = -76.6354664210025

x88 = -57.7859104994637

x89 = 4.08737859395935

x90 = 61.5946103369484

x90 = 61.5946103369484

Otras calculadoras

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Expresiones idénticas

Expresiones semejantes

2sin²x+3sinxcosx-8cos²x la ecuación

Solución numérica:

Solución