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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*(-2-y)-y-2=0
- Expresar {x} en función de y en la ecuación:
- -9*x-12*y=-19
- -8*x+3*y=-4
- 10*x+3*y=2
- -10*x-12*y=-10
- Suma de la serie:
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51
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Expresiones idénticas
- sqrt99×sinx-49cosx= cincuenta y uno
- raíz cuadrada de 99× seno de x menos 49 coseno de x es igual a 51
- raíz cuadrada de 99× seno de x menos 49 coseno de x es igual a cincuenta y uno
- √99×sinx-49cosx=51
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Expresiones semejantes
- sqrt99×sinx+49cosx=51
- 6(1+5x)=5(1+6x)
- 4(x+2)-5(1-x)-x-2=0
- x+(5x+2)^2=25(1+x^2)
sqrt99×sinx-49cosx=51 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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____ \/ 99 *sin(x) - 49*cos(x) = 51
$$\sqrt{99} \sin{\left(x \right)} - 49 \cos{\left(x \right)} = 51$$
Respuesta rápida
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/ / ____ _____\\ / / ____ _____\\
| |3*\/ 11 I*\/ 101 || | |3*\/ 11 I*\/ 101 ||
x1 = 2*re|atan|-------- - ---------|| + 2*I*im|atan|-------- - ---------||
\ \ 2 2 // \ \ 2 2 //
$$x_{1} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)}$$
/ / ____ _____\\ / / ____ _____\\
| |3*\/ 11 I*\/ 101 || | |3*\/ 11 I*\/ 101 ||
x2 = 2*re|atan|-------- + ---------|| + 2*I*im|atan|-------- + ---------||
\ \ 2 2 // \ \ 2 2 //
$$x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)}$$
x2 = 2*re(atan(3*sqrt(11)/2 + sqrt(101)*i/2)) + 2*i*im(atan(3*sqrt(11)/2 + sqrt(101)*i/2))
Suma y producto de raíces
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suma
/ / ____ _____\\ / / ____ _____\\ / / ____ _____\\ / / ____ _____\\
| |3*\/ 11 I*\/ 101 || | |3*\/ 11 I*\/ 101 || | |3*\/ 11 I*\/ 101 || | |3*\/ 11 I*\/ 101 ||
2*re|atan|-------- - ---------|| + 2*I*im|atan|-------- - ---------|| + 2*re|atan|-------- + ---------|| + 2*I*im|atan|-------- + ---------||
\ \ 2 2 // \ \ 2 2 // \ \ 2 2 // \ \ 2 2 //
$$\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)}\right)$$
=
/ / ____ _____\\ / / ____ _____\\ / / ____ _____\\ / / ____ _____\\
| |3*\/ 11 I*\/ 101 || | |3*\/ 11 I*\/ 101 || | |3*\/ 11 I*\/ 101 || | |3*\/ 11 I*\/ 101 ||
2*re|atan|-------- + ---------|| + 2*re|atan|-------- - ---------|| + 2*I*im|atan|-------- + ---------|| + 2*I*im|atan|-------- - ---------||
\ \ 2 2 // \ \ 2 2 // \ \ 2 2 // \ \ 2 2 //
$$2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)}$$
producto
/ / / ____ _____\\ / / ____ _____\\\ / / / ____ _____\\ / / ____ _____\\\ | | |3*\/ 11 I*\/ 101 || | |3*\/ 11 I*\/ 101 ||| | | |3*\/ 11 I*\/ 101 || | |3*\/ 11 I*\/ 101 ||| |2*re|atan|-------- - ---------|| + 2*I*im|atan|-------- - ---------|||*|2*re|atan|-------- + ---------|| + 2*I*im|atan|-------- + ---------||| \ \ \ 2 2 // \ \ 2 2 /// \ \ \ 2 2 // \ \ 2 2 ///
$$\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)}\right)$$
=
/ / / ____ _____\\ / / ____ _____\\\ / / / ____ _____\\ / / ____ _____\\\ | | |3*\/ 11 I*\/ 101 || | |3*\/ 11 I*\/ 101 ||| | | |3*\/ 11 I*\/ 101 || | |3*\/ 11 I*\/ 101 ||| 4*|I*im|atan|-------- + ---------|| + re|atan|-------- + ---------|||*|I*im|atan|-------- - ---------|| + re|atan|-------- - ---------||| \ \ \ 2 2 // \ \ 2 2 /// \ \ \ 2 2 // \ \ 2 2 ///
$$4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)}\right)$$
4*(i*im(atan(3*sqrt(11)/2 + i*sqrt(101)/2)) + re(atan(3*sqrt(11)/2 + i*sqrt(101)/2)))*(i*im(atan(3*sqrt(11)/2 - i*sqrt(101)/2)) + re(atan(3*sqrt(11)/2 - i*sqrt(101)/2)))
Respuesta numérica
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x1 = 2.94125781126667 - 0.199668157798415*i
x2 = 2.94125781126667 + 0.199668157798415*i
x2 = 2.94125781126667 + 0.199668157798415*i