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Ecuación 1/(x-3)^2-3/(x-3)-4=0
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Ecuación 9*(x-5)=-x
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Ecuación 13x+10=6x-4
- Ecuación x-y=1
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Expresiones idénticas
- (dos cosx/ dos -sqrt2)*(sin5x+2)= cero
- (2 coseno de x dividir por 2 menos raíz cuadrada de 2) multiplicar por ( seno de 5x más 2) es igual a 0
- (dos coseno de x dividir por dos menos raíz cuadrada de 2) multiplicar por ( seno de 5x más 2) es igual a cero
- (2cosx/2-√2)*(sin5x+2)=0
- (2cosx/2-sqrt2)(sin5x+2)=0
- 2cosx/2-sqrt2sin5x+2=0
- (2cosx/2-sqrt2)*(sin5x+2)=O
- (2cosx dividir por 2-sqrt2)*(sin5x+2)=0
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Expresiones semejantes
- (2cosx/2-sqrt2)*(sin5x-2)=0
- (2cosx/2+sqrt2)*(sin5x+2)=0
(2cosx/2-sqrt2)*(sin5x+2)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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/2*cos(x) ___\ |-------- - \/ 2 |*(sin(5*x) + 2) = 0 \ 2 /
$$\left(\frac{2 \cos{\left(x \right)}}{2} - \sqrt{2}\right) \left(\sin{\left(5 x \right)} + 2\right) = 0$$
Respuesta rápida
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/ / ___\\ / / ___\\
| |1 I*\/ 3 || | |1 I*\/ 3 ||
2*re|atan|- - -------|| 2*I*im|atan|- - -------||
\ \2 2 // \ \2 2 //
x1 = - ----------------------- - -------------------------
5 5
$$x_{1} = - \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5}$$
/ / ___\\ / / ___\\
| |1 I*\/ 3 || | |1 I*\/ 3 ||
2*re|atan|- + -------|| 2*I*im|atan|- + -------||
\ \2 2 // \ \2 2 //
x2 = - ----------------------- - -------------------------
5 5
$$x_{2} = - \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5}$$
/ ____________\
| / ___ |
|\/ -1 + \/ 2 |
x3 = -2*I*atanh|---------------|
| ___________|
| / ___ |
\ \/ 1 + \/ 2 /
$$x_{3} = - 2 i \operatorname{atanh}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)}$$
/ ____________\
| / ___ |
|\/ -1 + \/ 2 |
x4 = 2*I*atanh|---------------|
| ___________|
| / ___ |
\ \/ 1 + \/ 2 /
$$x_{4} = 2 i \operatorname{atanh}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)}$$
x4 = 2*i*atanh(sqrt(-1 + sqrt(2))/sqrt(1 + sqrt(2)))
Suma y producto de raíces
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suma
/ / ___\\ / / ___\\ / / ___\\ / / ___\\
| |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 // |\/ -1 + \/ 2 | |\/ -1 + \/ 2 |
- ----------------------- - ------------------------- + - ----------------------- - ------------------------- - 2*I*atanh|---------------| + 2*I*atanh|---------------|
5 5 5 5 | ___________| | ___________|
| / ___ | | / ___ |
\ \/ 1 + \/ 2 / \ \/ 1 + \/ 2 /
$$\left(\left(\left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5}\right) + \left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5}\right)\right) - 2 i \operatorname{atanh}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)}\right) + 2 i \operatorname{atanh}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)}$$
=
/ / ___\\ / / ___\\ / / ___\\ / / ___\\
| |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 //
- ----------------------- - ----------------------- - ------------------------- - -------------------------
5 5 5 5
$$- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5}$$
producto
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\
| | |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 //| |\/ -1 + \/ 2 | |\/ -1 + \/ 2 |
|- ----------------------- - -------------------------|*|- ----------------------- - -------------------------|*-2*I*atanh|---------------|*2*I*atanh|---------------|
\ 5 5 / \ 5 5 / | ___________| | ___________|
| / ___ | | / ___ |
\ \/ 1 + \/ 2 / \ \/ 1 + \/ 2 /
$$2 i \operatorname{atanh}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)} - 2 i \operatorname{atanh}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)} \left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5}\right) \left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5}\right)$$
=
/ ____________\
| / ___ | / / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\
2|\/ -1 + \/ 2 | | | |1 I*\/ 3 || | |1 I*\/ 3 ||| | | |1 I*\/ 3 || | |1 I*\/ 3 |||
16*atanh |---------------|*|I*im|atan|- + -------|| + re|atan|- + -------|||*|I*im|atan|- - -------|| + re|atan|- - -------|||
| ___________| \ \ \2 2 // \ \2 2 /// \ \ \2 2 // \ \2 2 ///
| / ___ |
\ \/ 1 + \/ 2 /
------------------------------------------------------------------------------------------------------------------------------
25
$$\frac{16 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right) \operatorname{atanh}^{2}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)}}{25}$$
16*atanh(sqrt(-1 + sqrt(2))/sqrt(1 + sqrt(2)))^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)))/25
Respuesta numérica
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x1 = -0.881373587019543*i
x2 = 0.881373587019543*i
x3 = -0.314159265358979 + 0.263391579384963*i
x4 = -0.314159265358979 - 0.263391579384963*i
x4 = -0.314159265358979 - 0.263391579384963*i