Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación (7x-8)-(4x-5)=15
-
Ecuación -3x-12=15
-
Ecuación x^3+2x^2-9x-18=0
-
Ecuación cosx=√2/2
- Expresar {x} en función de y en la ecuación:
- -6*x-17*y=14
- 5*x-2*y=-14
- 15*x+14*y=19
- -10*x-15*y=9
-
Expresiones idénticas
- sqrt(9a^ dos -b^ dos)
- raíz cuadrada de (9a al cuadrado menos b al cuadrado )
- raíz cuadrada de (9a en el grado dos menos b en el grado dos)
- √(9a^2-b^2)
- sqrt(9a2-b2)
- sqrt9a2-b2
- sqrt(9a²-b²)
- sqrt(9a en el grado 2-b en el grado 2)
- sqrt9a^2-b^2
-
Expresiones semejantes
- sqrt(9a^2+b^2)
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x^2-36)=8
- sqrt(x)=7.89
- sqrt(5x^2-20x+21)+sqrt(3x^2-12x+28)=8x-2x^2-3
- sqrt(2x+4)=x-2
- sqrt(2+log2(x))=log2(x)
sqrt(9a^2-b^2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$\sqrt{9 a^{2} - b^{2}} = 0$$
cambiamos
$$9 a^{2} - b^{2} = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$b_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$b_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = -1$$
$$b = 0$$
$$c = 9 a^{2}$$
, entonces
La ecuación tiene dos raíces.
o
$$b_{1} = - 3 \sqrt{a^{2}}$$
$$b_{2} = 3 \sqrt{a^{2}}$$
cambiamos
$$9 a^{2} - b^{2} = 0$$
Es la ecuación de la forma
a*b^2 + b*b + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$b_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$b_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = -1$$
$$b = 0$$
$$c = 9 a^{2}$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1) * (9*a^2) = 36*a^2
La ecuación tiene dos raíces.
b1 = (-b + sqrt(D)) / (2*a)
b2 = (-b - sqrt(D)) / (2*a)
o
$$b_{1} = - 3 \sqrt{a^{2}}$$
$$b_{2} = 3 \sqrt{a^{2}}$$
Gráfica
Respuesta rápida
[src]
______________________________________ ______________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/|
b1 = - 3*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *cos|-------------------------------------| - 3*I*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *sin|-------------------------------------|
\ 2 / \ 2 /
$$b_{1} = - 3 i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - 3 \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}$$
______________________________________ ______________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/|
b2 = 3*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *cos|-------------------------------------| + 3*I*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *sin|-------------------------------------|
\ 2 / \ 2 /
$$b_{2} = 3 i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 3 \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}$$
b2 = 3*i*((re(a)^2 - im(a)^2)^2 + 4*re(a)^2*im(a)^2)^(1/4)*sin(atan2(2*re(a)*im(a, re(a)^2 - im(a)^2)/2) + 3*((re(a)^2 - im(a)^2)^2 + 4*re(a)^2*im(a)^2)^(1/4)*cos(atan2(2*re(a)*im(a), re(a)^2 - im(a)^2)/2))
Suma y producto de raíces
[src]
suma
______________________________________ ______________________________________ ______________________________________ ______________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/|
- 3*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *cos|-------------------------------------| - 3*I*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *sin|-------------------------------------| + 3*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *cos|-------------------------------------| + 3*I*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *sin|-------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- 3 i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - 3 \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) + \left(3 i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 3 \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ ______________________________________ ______________________________________ \ / ______________________________________ ______________________________________ \ | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/|| | 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/| 4 / / 2 2 \ 2 2 |atan2\2*im(a)*re(a), re (a) - im (a)/|| |- 3*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *cos|-------------------------------------| - 3*I*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *sin|-------------------------------------||*|3*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *cos|-------------------------------------| + 3*I*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *sin|-------------------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- 3 i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - 3 \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) \left(3 i \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 3 \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right)$$
=
______________________________________
/ 2 / 2 2 \
/ / 2 2 \ 2 2 I*atan2\2*im(a)*re(a), re (a) - im (a)/
-9*\/ \re (a) - im (a)/ + 4*im (a)*re (a) *e
$$- 9 \sqrt{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}$$
-9*sqrt((re(a)^2 - im(a)^2)^2 + 4*im(a)^2*re(a)^2)*exp(i*atan2(2*im(a)*re(a), re(a)^2 - im(a)^2))