Sr Examen
Otras calculadoras
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¿Cómo usar?
- La ecuación:
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Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
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Ecuación x^2-14*x+33=0
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Ecuación 5(x-4)=3x-10
- Expresar {x} en función de y en la ecuación:
- 12*x+1*y=15
- -17*x-12*y=-9
- 18*x+17*y=-14
- 16*x-17*y=-15
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Expresiones idénticas
- Sqrt(a)*cosx- dos sinx=sqrt(dos)+sqrt(2-a)
- Sqrt(a) multiplicar por coseno de x menos 2 seno de x es igual a raíz cuadrada de (2) más raíz cuadrada de (2 menos a)
- Sqrt(a) multiplicar por coseno de x menos dos seno de x es igual a raíz cuadrada de (dos) más raíz cuadrada de (2 menos a)
- Sqrt(a)*cosx-2sinx=√(2)+√(2-a)
- Sqrt(a)cosx-2sinx=sqrt(2)+sqrt(2-a)
- Sqrtacosx-2sinx=sqrt2+sqrt2-a
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Expresiones semejantes
- Sqrt(a)*cosx+2sinx=sqrt(2)+sqrt(2-a)
- Sqrt(a)*cosx-2sinx=sqrt(2)-sqrt(2-a)
- Sqrt(a)*cosx-2sinx=sqrt(2)+sqrt(2+a)
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt^4(17x^2-16)=x
- sqrt(0,5+(sinx)^2)+c0s2x=1
- sqrt4(4x+5-x^2)-sqrt(4x-x^2-3)=1
- sqrt^4(x+15)+sqrt^4(1-x)=2
- sqrt(x-1)*sqrt(x+a^2)*sqrt(x-3)=0
- Raíz cuadrada sqrt
- sqrt^4(17x^2-16)=x
- sqrt(0,5+(sinx)^2)+c0s2x=1
- sqrt4(4x+5-x^2)-sqrt(4x-x^2-3)=1
- sqrt^4(x+15)+sqrt^4(1-x)=2
- sqrt(x-1)*sqrt(x+a^2)*sqrt(x-3)=0
Sqrt(a)*cosx-2sinx=sqrt(2)+sqrt(2-a) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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___ ___ _______ \/ a *cos(x) - 2*sin(x) = \/ 2 + \/ 2 - a
$$\sqrt{a} \cos{\left(x \right)} - 2 \sin{\left(x \right)} = \sqrt{2 - a} + \sqrt{2}$$
Gráfica
Suma y producto de raíces
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suma
/ / _____________________\\ / / _____________________\\ / / _____________________\\ / / _____________________\\
| | ___ / ___ _______ || | | ___ / ___ _______ || | | ___ / ___ _______ || | | ___ / ___ _______ ||
| |-2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a || | |-2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a || | |2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a || | |2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a ||
2*re|atan|-----------------------------------|| + 2*I*im|atan|-----------------------------------|| + - 2*re|atan|----------------------------------|| - 2*I*im|atan|----------------------------------||
| | ___ ___ _______ || | | ___ ___ _______ || | | ___ ___ _______ || | | ___ ___ _______ ||
\ \ \/ 2 + \/ a + \/ 2 - a // \ \ \/ 2 + \/ a + \/ 2 - a // \ \ \/ 2 + \/ a + \/ 2 - a // \ \ \/ 2 + \/ a + \/ 2 - a //
$$\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}\right)$$
=
/ / _____________________\\ / / _____________________\\ / / _____________________\\ / / _____________________\\
| | ___ / ___ _______ || | | ___ / ___ _______ || | | ___ / ___ _______ || | | ___ / ___ _______ ||
| |2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a || | |-2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a || | |2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a || | |-2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a ||
- 2*re|atan|----------------------------------|| + 2*re|atan|-----------------------------------|| - 2*I*im|atan|----------------------------------|| + 2*I*im|atan|-----------------------------------||
| | ___ ___ _______ || | | ___ ___ _______ || | | ___ ___ _______ || | | ___ ___ _______ ||
\ \ \/ 2 + \/ a + \/ 2 - a // \ \ \/ 2 + \/ a + \/ 2 - a // \ \ \/ 2 + \/ a + \/ 2 - a // \ \ \/ 2 + \/ a + \/ 2 - a //
$$2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}$$
producto
/ / / _____________________\\ / / _____________________\\\ / / / _____________________\\ / / _____________________\\\ | | | ___ / ___ _______ || | | ___ / ___ _______ ||| | | | ___ / ___ _______ || | | ___ / ___ _______ ||| | | |-2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a || | |-2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a ||| | | |2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a || | |2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a ||| |2*re|atan|-----------------------------------|| + 2*I*im|atan|-----------------------------------|||*|- 2*re|atan|----------------------------------|| - 2*I*im|atan|----------------------------------||| | | | ___ ___ _______ || | | ___ ___ _______ ||| | | | ___ ___ _______ || | | ___ ___ _______ ||| \ \ \ \/ 2 + \/ a + \/ 2 - a // \ \ \/ 2 + \/ a + \/ 2 - a /// \ \ \ \/ 2 + \/ a + \/ 2 - a // \ \ \/ 2 + \/ a + \/ 2 - a ///
$$\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}\right)$$
=
/ / / _____________________\\ / / _____________________\\\ / / / _____________________\\ / / _____________________\\\ | | | ___ / ___ _______ || | | ___ / ___ _______ ||| | | | ___ / ___ _______ || | | ___ / ___ _______ ||| | | |-2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a || | |-2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a ||| | | |2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a || | |2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a ||| -4*|I*im|atan|-----------------------------------|| + re|atan|-----------------------------------|||*|I*im|atan|----------------------------------|| + re|atan|----------------------------------||| | | | ___ ___ _______ || | | ___ ___ _______ ||| | | | ___ ___ _______ || | | ___ ___ _______ ||| \ \ \ \/ 2 + \/ a + \/ 2 - a // \ \ \/ 2 + \/ a + \/ 2 - a /// \ \ \ \/ 2 + \/ a + \/ 2 - a // \ \ \/ 2 + \/ a + \/ 2 - a ///
$$- 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}\right)$$
-4*(i*im(atan((-2 + sqrt(2)*sqrt(a - sqrt(2)*sqrt(2 - a)))/(sqrt(2) + sqrt(a) + sqrt(2 - a)))) + re(atan((-2 + sqrt(2)*sqrt(a - sqrt(2)*sqrt(2 - a)))/(sqrt(2) + sqrt(a) + sqrt(2 - a)))))*(i*im(atan((2 + sqrt(2)*sqrt(a - sqrt(2)*sqrt(2 - a)))/(sqrt(2) + sqrt(a) + sqrt(2 - a)))) + re(atan((2 + sqrt(2)*sqrt(a - sqrt(2)*sqrt(2 - a)))/(sqrt(2) + sqrt(a) + sqrt(2 - a)))))
Respuesta rápida
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/ / _____________________\\ / / _____________________\\
| | ___ / ___ _______ || | | ___ / ___ _______ ||
| |-2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a || | |-2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a ||
x1 = 2*re|atan|-----------------------------------|| + 2*I*im|atan|-----------------------------------||
| | ___ ___ _______ || | | ___ ___ _______ ||
\ \ \/ 2 + \/ a + \/ 2 - a // \ \ \/ 2 + \/ a + \/ 2 - a //
$$x_{1} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} - 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}$$
/ / _____________________\\ / / _____________________\\
| | ___ / ___ _______ || | | ___ / ___ _______ ||
| |2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a || | |2 + \/ 2 *\/ a - \/ 2 *\/ 2 - a ||
x2 = - 2*re|atan|----------------------------------|| - 2*I*im|atan|----------------------------------||
| | ___ ___ _______ || | | ___ ___ _______ ||
\ \ \/ 2 + \/ a + \/ 2 - a // \ \ \/ 2 + \/ a + \/ 2 - a //
$$x_{2} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{a - \sqrt{2} \sqrt{2 - a}} + 2}{\sqrt{a} + \sqrt{2 - a} + \sqrt{2}} \right)}\right)}$$
x2 = -2*re(atan((sqrt(2)*sqrt(a - sqrt(2)*sqrt(2 - a)) + 2)/(sqrt(a) + sqrt(2 - a) + sqrt(2)))) - 2*i*im(atan((sqrt(2)*sqrt(a - sqrt(2)*sqrt(2 - a)) + 2)/(sqrt(a) + sqrt(2 - a) + sqrt(2))))