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- La ecuación:
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Ecuación x^3-x^2-x-1=0
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Ecuación 3x-2(3x+4)=10
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Ecuación 12-4(x-3)=39-9x
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Ecuación 0,2x+2,7=1,4-1,1x
- Expresar {x} en función de y en la ecuación:
- -11*x-3*y=14
- 2*x-15*y=-1
- -18*x-6*y=-1
- 6*x+9*y=-9
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Expresiones idénticas
- sgrt(3sinx)+cosx= dos sin(x+π÷2)
- sgrt(3 seno de x) más coseno de x es igual a 2 seno de (x más π÷2)
- sgrt(3 seno de x) más coseno de x es igual a dos seno de (x más π÷2)
- sgrt3sinx+cosx=2sinx+π÷2
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Expresiones semejantes
- sgrt(3sinx)-cosx=2sin(x+π÷2)
- sgrt(3sinx)+cosx=2sin(x-π÷2)
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Expresiones con funciones
- sgrt
- Sgrt5x+3/2=45
- Sgrtx^2-5=sgrt4x
- sgrt(x-5)-sgrt(9-x)=1
- cosx
- cosx*cosx+(x-Pi/2)^(1/2)*cosx+(x-Pi/2)^(1/2)=0
- cosx=√3
- cosx⋅ctgx−(−√3/3)cosx=0
- Cosxcos2x-sin2xx=-1
- Cosx=2
sgrt(3sinx)+cosx=2sin(x+π÷2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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__________ / pi\
\/ 3*sin(x) + cos(x) = 2*sin|x + --|
\ 2 /
$$\sqrt{3 \sin{\left(x \right)}} + \cos{\left(x \right)} = 2 \sin{\left(x + \frac{\pi}{2} \right)}$$
Suma y producto de raíces
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suma
/ / ____________\\ / / ____________\\ / / ____________\\ / / ____________\\ / ____________\
| | ____ ___ / ____ || | | ____ ___ / ____ || | | ____ ___ / ____ || | | ____ ___ / ____ || | ____ ___ / ____ |
| | 3 \/ 13 \/ 6 *\/ 3 - \/ 13 || | | 3 \/ 13 \/ 6 *\/ 3 - \/ 13 || | |3 \/ 13 \/ 6 *\/ 3 - \/ 13 || | |3 \/ 13 \/ 6 *\/ 3 - \/ 13 || |3 \/ 13 \/ 6 *\/ 3 + \/ 13 |
- 2*re|atan|- - + ------ + ---------------------|| - 2*I*im|atan|- - + ------ + ---------------------|| + 2*re|atan|- - ------ + ---------------------|| + 2*I*im|atan|- - ------ + ---------------------|| + 2*atan|- + ------ - ---------------------|
\ \ 2 2 2 // \ \ 2 2 2 // \ \2 2 2 // \ \2 2 2 // \2 2 2 /
$$\left(\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{13}}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{13}}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{13}}{2} + \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{13}}{2} + \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)}\right)\right) + 2 \operatorname{atan}{\left(- \frac{\sqrt{6} \sqrt{3 + \sqrt{13}}}{2} + \frac{3}{2} + \frac{\sqrt{13}}{2} \right)}$$
=
/ / ____________\\ / ____________\ / / ____________\\ / / ____________\\ / / ____________\\
| | ____ ___ / ____ || | ____ ___ / ____ | | | ____ ___ / ____ || | | ____ ___ / ____ || | | ____ ___ / ____ ||
| | 3 \/ 13 \/ 6 *\/ 3 - \/ 13 || |3 \/ 13 \/ 6 *\/ 3 + \/ 13 | | |3 \/ 13 \/ 6 *\/ 3 - \/ 13 || | | 3 \/ 13 \/ 6 *\/ 3 - \/ 13 || | |3 \/ 13 \/ 6 *\/ 3 - \/ 13 ||
- 2*re|atan|- - + ------ + ---------------------|| + 2*atan|- + ------ - ---------------------| + 2*re|atan|- - ------ + ---------------------|| - 2*I*im|atan|- - + ------ + ---------------------|| + 2*I*im|atan|- - ------ + ---------------------||
\ \ 2 2 2 // \2 2 2 / \ \2 2 2 // \ \ 2 2 2 // \ \2 2 2 //
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{13}}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{13}}{2} + \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)} + 2 \operatorname{atan}{\left(- \frac{\sqrt{6} \sqrt{3 + \sqrt{13}}}{2} + \frac{3}{2} + \frac{\sqrt{13}}{2} \right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{13}}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{13}}{2} + \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)}$$
producto
/ / / ____________\\ / / ____________\\\ / / / ____________\\ / / ____________\\\ / ____________\ | | | ____ ___ / ____ || | | ____ ___ / ____ ||| | | | ____ ___ / ____ || | | ____ ___ / ____ ||| | ____ ___ / ____ | | | | 3 \/ 13 \/ 6 *\/ 3 - \/ 13 || | | 3 \/ 13 \/ 6 *\/ 3 - \/ 13 ||| | | |3 \/ 13 \/ 6 *\/ 3 - \/ 13 || | |3 \/ 13 \/ 6 *\/ 3 - \/ 13 ||| |3 \/ 13 \/ 6 *\/ 3 + \/ 13 | |- 2*re|atan|- - + ------ + ---------------------|| - 2*I*im|atan|- - + ------ + ---------------------|||*|2*re|atan|- - ------ + ---------------------|| + 2*I*im|atan|- - ------ + ---------------------|||*2*atan|- + ------ - ---------------------| \ \ \ 2 2 2 // \ \ 2 2 2 /// \ \ \2 2 2 // \ \2 2 2 /// \2 2 2 /
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{13}}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{13}}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{13}}{2} + \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{13}}{2} + \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)}\right) 2 \operatorname{atan}{\left(- \frac{\sqrt{6} \sqrt{3 + \sqrt{13}}}{2} + \frac{3}{2} + \frac{\sqrt{13}}{2} \right)}$$
=
/ / / ____________\\ / / ____________\\\ / / / ____________\\ / / ____________\\\ / ____________\ | | | ____ ___ / ____ || | | ____ ___ / ____ ||| | | | ____ ___ / ____ || | | ____ ___ / ____ ||| | ____ ___ / ____ | | | | 3 \/ 13 \/ 6 *\/ 3 - \/ 13 || | | 3 \/ 13 \/ 6 *\/ 3 - \/ 13 ||| | | |3 \/ 13 \/ 6 *\/ 3 - \/ 13 || | |3 \/ 13 \/ 6 *\/ 3 - \/ 13 ||| |3 \/ 13 \/ 6 *\/ 3 + \/ 13 | -8*|I*im|atan|- - + ------ + ---------------------|| + re|atan|- - + ------ + ---------------------|||*|I*im|atan|- - ------ + ---------------------|| + re|atan|- - ------ + ---------------------|||*atan|- + ------ - ---------------------| \ \ \ 2 2 2 // \ \ 2 2 2 /// \ \ \2 2 2 // \ \2 2 2 /// \2 2 2 /
$$- 8 \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{13}}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{13}}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{13}}{2} + \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{13}}{2} + \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)}\right) \operatorname{atan}{\left(- \frac{\sqrt{6} \sqrt{3 + \sqrt{13}}}{2} + \frac{3}{2} + \frac{\sqrt{13}}{2} \right)}$$
-8*(i*im(atan(-3/2 + sqrt(13)/2 + sqrt(6)*sqrt(3 - sqrt(13))/2)) + re(atan(-3/2 + sqrt(13)/2 + sqrt(6)*sqrt(3 - sqrt(13))/2)))*(i*im(atan(3/2 - sqrt(13)/2 + sqrt(6)*sqrt(3 - sqrt(13))/2)) + re(atan(3/2 - sqrt(13)/2 + sqrt(6)*sqrt(3 - sqrt(13))/2)))*atan(3/2 + sqrt(13)/2 - sqrt(6)*sqrt(3 + sqrt(13))/2)
Respuesta rápida
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/ / ____________\\ / / ____________\\
| | ____ ___ / ____ || | | ____ ___ / ____ ||
| | 3 \/ 13 \/ 6 *\/ 3 - \/ 13 || | | 3 \/ 13 \/ 6 *\/ 3 - \/ 13 ||
x1 = - 2*re|atan|- - + ------ + ---------------------|| - 2*I*im|atan|- - + ------ + ---------------------||
\ \ 2 2 2 // \ \ 2 2 2 //
$$x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{13}}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{13}}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)}$$
/ / ____________\\ / / ____________\\
| | ____ ___ / ____ || | | ____ ___ / ____ ||
| |3 \/ 13 \/ 6 *\/ 3 - \/ 13 || | |3 \/ 13 \/ 6 *\/ 3 - \/ 13 ||
x2 = 2*re|atan|- - ------ + ---------------------|| + 2*I*im|atan|- - ------ + ---------------------||
\ \2 2 2 // \ \2 2 2 //
$$x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{13}}{2} + \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{13}}{2} + \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{13}}}{2} \right)}\right)}$$
/ ____________\
| ____ ___ / ____ |
|3 \/ 13 \/ 6 *\/ 3 + \/ 13 |
x3 = 2*atan|- + ------ - ---------------------|
\2 2 2 /
$$x_{3} = 2 \operatorname{atan}{\left(- \frac{\sqrt{6} \sqrt{3 + \sqrt{13}}}{2} + \frac{3}{2} + \frac{\sqrt{13}}{2} \right)}$$
x3 = 2*atan(-sqrt(6)*sqrt(3 + sqrt(13))/2 + 3/2 + sqrt(13)/2)
Respuesta numérica
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x1 = -43.6746935007264
x2 = 0.307603649530711
x3 = -12.2587669648285
x4 = -93.9401759581631
x5 = 25.4403448782491
x6 = -81.3738053438039
x7 = -56.2410641150856
x8 = 38.0067154926082
x9 = 75.7058273356858
x10 = 69.4226420285062
x11 = 19.1571595710695
x12 = -75.0906200366243
x13 = -100.223361265343
x14 = 100.838568564404
x15 = 94.5553832572245
x16 = 12.8739742638899
x17 = -68.8074347294447
x18 = 31.7235301854286
x19 = -37.3915081935468
x20 = 6.5907889567103
x21 = 50.5730861069674
x22 = 63.1394567213266
x23 = 56.856271414147
x24 = -62.5242494222652
x25 = -18.541952272008
x26 = 81.9890126428653
x27 = -49.957878807906
x28 = -87.6569906509835
x29 = -31.1083228863672
x30 = 44.2899007997878
x31 = 88.2721979500449
x32 = -5.97558165764887
x33 = -24.8251375791876
x33 = -24.8251375791876