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- La ecuación:
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Ecuación 6*x^2+x-7=0
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Ecuación 2-5(3+2x)=17
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Ecuación (6*x+8)/2+5=5*x/3
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Ecuación 2+3x=−2x−13
- Expresar {x} en función de y en la ecuación:
- 6*x+4*y=15
- -4*x+4*y=-9
- 3*x-12*y=-14
- 1*x+4*y=-16
- Derivada de:
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sin(x)^(4)+cos(x)^(4)
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Expresiones idénticas
- sin(x)^(cuatro)+cos(x)^(cuatro)= uno - cero .5sin(dos x)^2
- seno de (x) en el grado (4) más coseno de (x) en el grado (4) es igual a 1 menos 0.5 seno de (2x) al cuadrado
- seno de (x) en el grado (cuatro) más coseno de (x) en el grado (cuatro) es igual a uno menos cero .5 seno de (dos x) al cuadrado
- sin(x)(4)+cos(x)(4)=1-0.5sin(2x)2
- sinx4+cosx4=1-0.5sin2x2
- sin(x)^(4)+cos(x)^(4)=1-0.5sin(2x)²
- sin(x) en el grado (4)+cos(x) en el grado (4)=1-0.5sin(2x) en el grado 2
- sinx^4+cosx^4=1-0.5sin2x^2
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Expresiones semejantes
- sin(x)^(4)+cos(x)^(4)=1+0.5sin(2x)^2
- sin(x)^(4)-cos(x)^(4)=1-0.5sin(2x)^2
- sinx^(4)+cosx^(4)=1-0.5sin(2x)^2
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Expresiones con funciones
- Seno sin
- sin(x/2)=(1/2)
- sin7xcosx-cos7xsinx=0
- sin(2*x)=cos(x-3*pi/2)
- sin(x*35/2)/(x*35/2)=0
- sin(x+3*pi/2)^2=cos(x)
- Coseno cos
- cos(2pi×x)-3sin(pi×x)+1=0
- cos(x+(|x|))=1
- cos(x-3/4)=0
- cos(x)=-0,7
- cos(y)=x-3
sin(x)^(4)+cos(x)^(4)=1-0.5sin(2x)^2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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2
4 4 sin (2*x)
sin (x) + cos (x) = 1 - ---------
2
$$\sin^{4}{\left(x \right)} + \cos^{4}{\left(x \right)} = 1 - \frac{\sin^{2}{\left(2 x \right)}}{2}$$
Suma y producto de raíces
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suma
/ ___________ ___________\ / ___________ ___________\ / ___________ ___________ \ / / ___________ ___________\ \
| / ___ / ___ | | / ___ / ___ | | / ___ / ___ | | | / ___ / ___ | |
7*pi 3*pi 3*pi pi pi pi 5*pi 3*pi |\/ 2 + \/ 2 + \/ 2 - \/ 2 | / / ___\ \ |\/ 2 - \/ 2 - \/ 2 + \/ 2 | / / ___\ \ | \/ 2 + \/ 2 - \/ 2 - \/ 2 | / / ___\ \ |-\- \/ 2 + \/ 2 - \/ 2 - \/ 2 / | / / ___\ \
- ---- - ---- - pi - ---- - -- + -- + -- + pi + ---- + ---- + 2*pi + 2*atan|-------------------------------| + I*\- 2*log\2*\/ 2 / + log(8)/ + 2*atan|-------------------------------| + I*\- 2*log\2*\/ 2 / + log(8)/ + 2*pi + 2*atan|---------------------------------| + I*\- 2*log\2*\/ 2 / + log(8)/ + -2*pi - 2*atan|-------------------------------------| + I*\- 2*log\2*\/ 2 / + log(8)/
4 2 4 2 4 2 4 2 | ___________ ___________| | ___________ ___________| | ___________ ___________| | ___________ ___________ |
| / ___ / ___ | | / ___ / ___ | | / ___ / ___ | | / ___ / ___ |
\\/ 2 + \/ 2 - \/ 2 - \/ 2 / \\/ 2 + \/ 2 + \/ 2 - \/ 2 / \- \/ 2 + \/ 2 - \/ 2 - \/ 2 / \ \/ 2 - \/ 2 - \/ 2 + \/ 2 /
$$\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(- \frac{7 \pi}{4} - \frac{3 \pi}{2}\right) - \pi\right) - \frac{3 \pi}{4}\right) - \frac{\pi}{2}\right) + \frac{\pi}{4}\right) + \frac{\pi}{2}\right) + \pi\right) + \frac{5 \pi}{4}\right) + \frac{3 \pi}{2}\right) + 2 \pi\right) + \left(2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)\right)\right) + \left(2 \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)\right)\right) + \left(2 \operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + 2 \pi + i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)\right)\right) + \left(- 2 \pi - 2 \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)\right)$$
=
/ / ___________ ___________\ \ / ___________ ___________\ / ___________ ___________\ / ___________ ___________ \
| | / ___ / ___ | | | / ___ / ___ | | / ___ / ___ | | / ___ / ___ |
|-\- \/ 2 + \/ 2 - \/ 2 - \/ 2 / | |\/ 2 - \/ 2 - \/ 2 + \/ 2 | |\/ 2 + \/ 2 + \/ 2 - \/ 2 | | \/ 2 + \/ 2 - \/ 2 - \/ 2 | / / ___\ \
pi - 2*atan|-------------------------------------| + 2*atan|-------------------------------| + 2*atan|-------------------------------| + 2*atan|---------------------------------| + 4*I*\- 2*log\2*\/ 2 / + log(8)/
| ___________ ___________ | | ___________ ___________| | ___________ ___________| | ___________ ___________|
| / ___ / ___ | | / ___ / ___ | | / ___ / ___ | | / ___ / ___ |
\ \/ 2 - \/ 2 - \/ 2 + \/ 2 / \\/ 2 + \/ 2 + \/ 2 - \/ 2 / \\/ 2 + \/ 2 - \/ 2 - \/ 2 / \- \/ 2 + \/ 2 - \/ 2 - \/ 2 /
$$2 \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + 2 \operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} - 2 \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + \pi + 4 i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)$$
producto
/ / ___________ ___________\ \ / / ___________ ___________\ \ / / ___________ ___________ \ \ / / / ___________ ___________\ \ \
| | / ___ / ___ | | | | / ___ / ___ | | | | / ___ / ___ | | | | | / ___ / ___ | | |
-7*pi -3*pi -3*pi -pi pi pi 5*pi 3*pi | |\/ 2 + \/ 2 + \/ 2 - \/ 2 | / / ___\ \| | |\/ 2 - \/ 2 - \/ 2 + \/ 2 | / / ___\ \| | | \/ 2 + \/ 2 - \/ 2 - \/ 2 | / / ___\ \| | |-\- \/ 2 + \/ 2 - \/ 2 - \/ 2 / | / / ___\ \|
0*-----*-----*(-pi)*-----*----*--*--*pi*----*----*2*pi*|2*atan|-------------------------------| + I*\- 2*log\2*\/ 2 / + log(8)/|*|2*atan|-------------------------------| + I*\- 2*log\2*\/ 2 / + log(8)/|*|2*pi + 2*atan|---------------------------------| + I*\- 2*log\2*\/ 2 / + log(8)/|*|-2*pi - 2*atan|-------------------------------------| + I*\- 2*log\2*\/ 2 / + log(8)/|
4 2 4 2 4 2 4 2 | | ___________ ___________| | | | ___________ ___________| | | | ___________ ___________| | | | ___________ ___________ | |
| | / ___ / ___ | | | | / ___ / ___ | | | | / ___ / ___ | | | | / ___ / ___ | |
\ \\/ 2 + \/ 2 - \/ 2 - \/ 2 / / \ \\/ 2 + \/ 2 + \/ 2 - \/ 2 / / \ \- \/ 2 + \/ 2 - \/ 2 - \/ 2 / / \ \ \/ 2 - \/ 2 - \/ 2 + \/ 2 / /
$$2 \pi \frac{3 \pi}{2} \frac{5 \pi}{4} \pi \frac{\pi}{2} \frac{\pi}{4} \cdot - \frac{\pi}{2} \cdot - \frac{3 \pi}{4} \cdot - \pi - \frac{3 \pi}{2} \cdot 0 \left(- \frac{7 \pi}{4}\right) \left(2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)\right) \left(2 \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)\right) \left(2 \operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + 2 \pi + i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)\right) \left(- 2 \pi - 2 \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)\right)$$
=
0
$$0$$
0
Respuesta rápida
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x1 = 0
$$x_{1} = 0$$
-7*pi
x2 = -----
4
$$x_{2} = - \frac{7 \pi}{4}$$
-3*pi
x3 = -----
2
$$x_{3} = - \frac{3 \pi}{2}$$
x4 = -pi
$$x_{4} = - \pi$$
-3*pi
x5 = -----
4
$$x_{5} = - \frac{3 \pi}{4}$$
-pi
x6 = ----
2
$$x_{6} = - \frac{\pi}{2}$$
pi
x7 = --
4
$$x_{7} = \frac{\pi}{4}$$
pi
x8 = --
2
$$x_{8} = \frac{\pi}{2}$$
x9 = pi
$$x_{9} = \pi$$
5*pi
x10 = ----
4
$$x_{10} = \frac{5 \pi}{4}$$
3*pi
x11 = ----
2
$$x_{11} = \frac{3 \pi}{2}$$
x12 = 2*pi
$$x_{12} = 2 \pi$$
/ ___________ ___________\
| / ___ / ___ |
|\/ 2 + \/ 2 + \/ 2 - \/ 2 | / / ___\ \
x13 = 2*atan|-------------------------------| + I*\- 2*log\2*\/ 2 / + log(8)/
| ___________ ___________|
| / ___ / ___ |
\\/ 2 + \/ 2 - \/ 2 - \/ 2 /
$$x_{13} = 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)$$
/ ___________ ___________\
| / ___ / ___ |
|\/ 2 - \/ 2 - \/ 2 + \/ 2 | / / ___\ \
x14 = 2*atan|-------------------------------| + I*\- 2*log\2*\/ 2 / + log(8)/
| ___________ ___________|
| / ___ / ___ |
\\/ 2 + \/ 2 + \/ 2 - \/ 2 /
$$x_{14} = 2 \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)$$
/ ___________ ___________ \
| / ___ / ___ |
| \/ 2 + \/ 2 - \/ 2 - \/ 2 | / / ___\ \
x15 = 2*pi + 2*atan|---------------------------------| + I*\- 2*log\2*\/ 2 / + log(8)/
| ___________ ___________|
| / ___ / ___ |
\- \/ 2 + \/ 2 - \/ 2 - \/ 2 /
$$x_{15} = 2 \operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + 2 \pi + i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)$$
/ / ___________ ___________\ \
| | / ___ / ___ | |
|-\- \/ 2 + \/ 2 - \/ 2 - \/ 2 / | / / ___\ \
x16 = -2*pi - 2*atan|-------------------------------------| + I*\- 2*log\2*\/ 2 / + log(8)/
| ___________ ___________ |
| / ___ / ___ |
\ \/ 2 - \/ 2 - \/ 2 + \/ 2 /
$$x_{16} = - 2 \pi - 2 \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- 2 \log{\left(2 \sqrt{2} \right)} + \log{\left(8 \right)}\right)$$
x16 = -2*pi - 2*atan(-(-sqrt(sqrt(2) + 2) - sqrt(2 - sqrt(2)))/(-sqrt(sqrt(2) + 2) + sqrt(2 - sqrt(2)))) + i*(-2*log(2*sqrt(2)) + log(8))
Respuesta numérica
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x1 = 66.0
x2 = -93.75
x3 = 93.75
x4 = 46.0
x5 = -51.9166666666667
x6 = -46.0
x7 = 18.0
x8 = -82.0
x9 = 16.25
x10 = -42.0
x11 = 64.0
x12 = 36.0
x13 = -66.0
x14 = -8.0
x15 = -26.0
x16 = 86.0
x17 = 98.25
x18 = 96.1666666666667
x19 = 42.0
x20 = -36.0
x21 = 100.0
x22 = -18.0
x23 = 74.25
x24 = -67.8333333333333
x25 = 90.0
x26 = -88.0
x27 = -92.0
x28 = -95.75
x29 = -27.75
x30 = 6.0
x31 = 78.0833333333333
x32 = -59.75
x33 = -84.0
x34 = 10.0
x35 = 62.0
x36 = 14.0
x37 = 34.25
x38 = 52.2037037037037
x39 = -14.0
x40 = -72.0
x41 = 0.0
x42 = -20.0
x43 = -75.75
x44 = 54.0
x45 = 2.25
x46 = 32.0
x47 = 76.25
x48 = 68.25
x49 = -40.0
x50 = -48.0
x51 = -77.75
x52 = -6.0
x53 = 60.25
x54 = 4.0
x55 = 44.25
x56 = -56.0
x57 = -10.0
x58 = -62.0
x59 = -58.0
x60 = 38.1666666666667
x61 = 84.0
x62 = -33.75
x63 = -86.0
x64 = -4.0
x65 = 40.0
x66 = -70.0
x67 = 8.0
x68 = 30.25
x69 = 82.0
x70 = -80.0
x71 = -49.7777777777778
x72 = -29.75
x73 = -32.0
x74 = -15.6666666666667
x75 = -24.25
x76 = -54.0
x77 = 48.0
x78 = -73.75
x79 = 20.0
x80 = 56.0
x81 = 58.0
x82 = 22.25
x83 = 70.0
x84 = 92.0
x85 = -90.0
x86 = 72.0
x87 = 88.0
x88 = -97.75
x89 = -64.0
x90 = 24.25
x91 = -100.0
x92 = 80.0
x93 = 26.0
x93 = 26.0