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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
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Expresiones idénticas
- log dos 2v−4log2v=− treinta y dos *x^2+ seis *x+ nueve = cero
- logaritmo de 22v−4 logaritmo de 2v es igual a −32 multiplicar por x al cuadrado más 6 multiplicar por x más 9 es igual a 0
- logaritmo de dos 2v−4 logaritmo de 2v es igual a − treinta y dos multiplicar por x al cuadrado más seis multiplicar por x más nueve es igual a cero
- log22v−4log2v=−32*x2+6*x+9=0
- log22v−4log2v=−32*x²+6*x+9=0
- log22v−4log2v=−32*x en el grado 2+6*x+9=0
- log22v−4log2v=−32x^2+6x+9=0
- log22v−4log2v=−32x2+6x+9=0
- log22v−4log2v=−32*x^2+6*x+9=O
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Expresiones semejantes
- log22v−4log2v=−32*x^2-6*x+9=0
- log22v−4log2v=−32*x^2+6*x-9=0
log22v−4log2v=−32*x^2+6*x+9=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 log(22*v) - 4*log(2*v) = - 32*x + 6*x + 9
$$- 4 \log{\left(2 v \right)} + \log{\left(22 v \right)} = \left(- 32 x^{2} + 6 x\right) + 9$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$- 4 \log{\left(2 v \right)} + \log{\left(22 v \right)} = \left(- 32 x^{2} + 6 x\right) + 9$$
en
$$\left(\left(32 x^{2} - 6 x\right) - 9\right) + \left(- 4 \log{\left(2 v \right)} + \log{\left(22 v \right)}\right) = 0$$
Abramos la expresión en la ecuación
$$\left(\left(32 x^{2} - 6 x\right) - 9\right) + \left(- 4 \log{\left(2 v \right)} + \log{\left(22 v \right)}\right) = 0$$
Obtenemos la ecuación cuadrática
$$32 x^{2} - 6 x - 3 \log{\left(v \right)} - 9 - 4 \log{\left(2 \right)} + \log{\left(22 \right)} = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 32$$
$$b = -6$$
$$c = - 3 \log{\left(v \right)} - 9 - 4 \log{\left(2 \right)} + \log{\left(22 \right)}$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{\sqrt{384 \log{\left(v \right)} - 128 \log{\left(22 \right)} + 512 \log{\left(2 \right)} + 1188}}{64} + \frac{3}{32}$$
$$x_{2} = \frac{3}{32} - \frac{\sqrt{384 \log{\left(v \right)} - 128 \log{\left(22 \right)} + 512 \log{\left(2 \right)} + 1188}}{64}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$- 4 \log{\left(2 v \right)} + \log{\left(22 v \right)} = \left(- 32 x^{2} + 6 x\right) + 9$$
en
$$\left(\left(32 x^{2} - 6 x\right) - 9\right) + \left(- 4 \log{\left(2 v \right)} + \log{\left(22 v \right)}\right) = 0$$
Abramos la expresión en la ecuación
$$\left(\left(32 x^{2} - 6 x\right) - 9\right) + \left(- 4 \log{\left(2 v \right)} + \log{\left(22 v \right)}\right) = 0$$
Obtenemos la ecuación cuadrática
$$32 x^{2} - 6 x - 3 \log{\left(v \right)} - 9 - 4 \log{\left(2 \right)} + \log{\left(22 \right)} = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 32$$
$$b = -6$$
$$c = - 3 \log{\left(v \right)} - 9 - 4 \log{\left(2 \right)} + \log{\left(22 \right)}$$
, entonces
D = b^2 - 4 * a * c =
(-6)^2 - 4 * (32) * (-9 - 4*log(2) - 3*log(v) + log(22)) = 1188 - 128*log(22) + 384*log(v) + 512*log(2)
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{\sqrt{384 \log{\left(v \right)} - 128 \log{\left(22 \right)} + 512 \log{\left(2 \right)} + 1188}}{64} + \frac{3}{32}$$
$$x_{2} = \frac{3}{32} - \frac{\sqrt{384 \log{\left(v \right)} - 128 \log{\left(22 \right)} + 512 \log{\left(2 \right)} + 1188}}{64}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$- 4 \log{\left(2 v \right)} + \log{\left(22 v \right)} = \left(- 32 x^{2} + 6 x\right) + 9$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{3 x}{16} - \frac{\log{\left(2 v \right)}}{8} + \frac{\log{\left(22 v \right)}}{32} - \frac{9}{32} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{3}{16}$$
$$q = \frac{c}{a}$$
$$q = - \frac{\log{\left(2 v \right)}}{8} + \frac{\log{\left(22 v \right)}}{32} - \frac{9}{32}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{3}{16}$$
$$x_{1} x_{2} = - \frac{\log{\left(2 v \right)}}{8} + \frac{\log{\left(22 v \right)}}{32} - \frac{9}{32}$$
$$- 4 \log{\left(2 v \right)} + \log{\left(22 v \right)} = \left(- 32 x^{2} + 6 x\right) + 9$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{3 x}{16} - \frac{\log{\left(2 v \right)}}{8} + \frac{\log{\left(22 v \right)}}{32} - \frac{9}{32} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{3}{16}$$
$$q = \frac{c}{a}$$
$$q = - \frac{\log{\left(2 v \right)}}{8} + \frac{\log{\left(22 v \right)}}{32} - \frac{9}{32}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{3}{16}$$
$$x_{1} x_{2} = - \frac{\log{\left(2 v \right)}}{8} + \frac{\log{\left(22 v \right)}}{32} - \frac{9}{32}$$
Gráfica
Respuesta rápida
[src]
_______________________________________________________________________________ / / / 79228162514264337593543950336 \\\ _______________________________________________________________________________ / / / 79228162514264337593543950336 \\\
/ 2 |atan2|96*arg(v), 297 + 96*log(|v|) + log|----------------------------------||| / 2 |atan2|96*arg(v), 297 + 96*log(|v|) + log|----------------------------------|||
/ / / 79228162514264337593543950336 \\ 2 | \ \2111377674535255285545615254209921//| / / / 79228162514264337593543950336 \\ 2 | \ \2111377674535255285545615254209921//|
4 / |297 + 96*log(|v|) + log|----------------------------------|| + 9216*arg (v) *cos|-----------------------------------------------------------------------------| I*4 / |297 + 96*log(|v|) + log|----------------------------------|| + 9216*arg (v) *sin|-----------------------------------------------------------------------------|
3 \/ \ \2111377674535255285545615254209921// \ 2 / \/ \ \2111377674535255285545615254209921// \ 2 /
x1 = -- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------
32 32 32
$$x_{1} = - \frac{i \sqrt[4]{\left(96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297\right)^{2} + 9216 \arg^{2}{\left(v \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(96 \arg{\left(v \right)},96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297 \right)}}{2} \right)}}{32} - \frac{\sqrt[4]{\left(96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297\right)^{2} + 9216 \arg^{2}{\left(v \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(96 \arg{\left(v \right)},96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297 \right)}}{2} \right)}}{32} + \frac{3}{32}$$
_______________________________________________________________________________ / / / 79228162514264337593543950336 \\\ _______________________________________________________________________________ / / / 79228162514264337593543950336 \\\
/ 2 |atan2|96*arg(v), 297 + 96*log(|v|) + log|----------------------------------||| / 2 |atan2|96*arg(v), 297 + 96*log(|v|) + log|----------------------------------|||
/ / / 79228162514264337593543950336 \\ 2 | \ \2111377674535255285545615254209921//| / / / 79228162514264337593543950336 \\ 2 | \ \2111377674535255285545615254209921//|
4 / |297 + 96*log(|v|) + log|----------------------------------|| + 9216*arg (v) *cos|-----------------------------------------------------------------------------| I*4 / |297 + 96*log(|v|) + log|----------------------------------|| + 9216*arg (v) *sin|-----------------------------------------------------------------------------|
3 \/ \ \2111377674535255285545615254209921// \ 2 / \/ \ \2111377674535255285545615254209921// \ 2 /
x2 = -- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------
32 32 32
$$x_{2} = \frac{i \sqrt[4]{\left(96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297\right)^{2} + 9216 \arg^{2}{\left(v \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(96 \arg{\left(v \right)},96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297 \right)}}{2} \right)}}{32} + \frac{\sqrt[4]{\left(96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297\right)^{2} + 9216 \arg^{2}{\left(v \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(96 \arg{\left(v \right)},96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297 \right)}}{2} \right)}}{32} + \frac{3}{32}$$
x2 = i*((96*log(|v|) + log(79228162514264337593543950336/2111377674535255285545615254209921) + 297)^2 + 9216*arg(v)^2)^(1/4)*sin(atan2(96*arg(v, 96*log(|v|) + log(79228162514264337593543950336/2111377674535255285545615254209921) + 297)/2)/32 + ((96*log(|v|) + log(79228162514264337593543950336/2111377674535255285545615254209921) + 297)^2 + 9216*arg(v)^2)^(1/4)*cos(atan2(96*arg(v), 96*log(|v|) + log(79228162514264337593543950336/2111377674535255285545615254209921) + 297)/2)/32 + 3/32)
Suma y producto de raíces
[src]
suma
_______________________________________________________________________________ / / / 79228162514264337593543950336 \\\ _______________________________________________________________________________ / / / 79228162514264337593543950336 \\\ _______________________________________________________________________________ / / / 79228162514264337593543950336 \\\ _______________________________________________________________________________ / / / 79228162514264337593543950336 \\\
/ 2 |atan2|96*arg(v), 297 + 96*log(|v|) + log|----------------------------------||| / 2 |atan2|96*arg(v), 297 + 96*log(|v|) + log|----------------------------------||| / 2 |atan2|96*arg(v), 297 + 96*log(|v|) + log|----------------------------------||| / 2 |atan2|96*arg(v), 297 + 96*log(|v|) + log|----------------------------------|||
/ / / 79228162514264337593543950336 \\ 2 | \ \2111377674535255285545615254209921//| / / / 79228162514264337593543950336 \\ 2 | \ \2111377674535255285545615254209921//| / / / 79228162514264337593543950336 \\ 2 | \ \2111377674535255285545615254209921//| / / / 79228162514264337593543950336 \\ 2 | \ \2111377674535255285545615254209921//|
4 / |297 + 96*log(|v|) + log|----------------------------------|| + 9216*arg (v) *cos|-----------------------------------------------------------------------------| I*4 / |297 + 96*log(|v|) + log|----------------------------------|| + 9216*arg (v) *sin|-----------------------------------------------------------------------------| 4 / |297 + 96*log(|v|) + log|----------------------------------|| + 9216*arg (v) *cos|-----------------------------------------------------------------------------| I*4 / |297 + 96*log(|v|) + log|----------------------------------|| + 9216*arg (v) *sin|-----------------------------------------------------------------------------|
3 \/ \ \2111377674535255285545615254209921// \ 2 / \/ \ \2111377674535255285545615254209921// \ 2 / 3 \/ \ \2111377674535255285545615254209921// \ 2 / \/ \ \2111377674535255285545615254209921// \ 2 /
-- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------
32 32 32 32 32 32
$$\left(- \frac{i \sqrt[4]{\left(96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297\right)^{2} + 9216 \arg^{2}{\left(v \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(96 \arg{\left(v \right)},96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297 \right)}}{2} \right)}}{32} - \frac{\sqrt[4]{\left(96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297\right)^{2} + 9216 \arg^{2}{\left(v \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(96 \arg{\left(v \right)},96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297 \right)}}{2} \right)}}{32} + \frac{3}{32}\right) + \left(\frac{i \sqrt[4]{\left(96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297\right)^{2} + 9216 \arg^{2}{\left(v \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(96 \arg{\left(v \right)},96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297 \right)}}{2} \right)}}{32} + \frac{\sqrt[4]{\left(96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297\right)^{2} + 9216 \arg^{2}{\left(v \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(96 \arg{\left(v \right)},96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297 \right)}}{2} \right)}}{32} + \frac{3}{32}\right)$$
=
3/16
$$\frac{3}{16}$$
producto
/ _______________________________________________________________________________ / / / 79228162514264337593543950336 \\\ _______________________________________________________________________________ / / / 79228162514264337593543950336 \\\\ / _______________________________________________________________________________ / / / 79228162514264337593543950336 \\\ _______________________________________________________________________________ / / / 79228162514264337593543950336 \\\\ | / 2 |atan2|96*arg(v), 297 + 96*log(|v|) + log|----------------------------------||| / 2 |atan2|96*arg(v), 297 + 96*log(|v|) + log|----------------------------------|||| | / 2 |atan2|96*arg(v), 297 + 96*log(|v|) + log|----------------------------------||| / 2 |atan2|96*arg(v), 297 + 96*log(|v|) + log|----------------------------------|||| | / / / 79228162514264337593543950336 \\ 2 | \ \2111377674535255285545615254209921//| / / / 79228162514264337593543950336 \\ 2 | \ \2111377674535255285545615254209921//|| | / / / 79228162514264337593543950336 \\ 2 | \ \2111377674535255285545615254209921//| / / / 79228162514264337593543950336 \\ 2 | \ \2111377674535255285545615254209921//|| | 4 / |297 + 96*log(|v|) + log|----------------------------------|| + 9216*arg (v) *cos|-----------------------------------------------------------------------------| I*4 / |297 + 96*log(|v|) + log|----------------------------------|| + 9216*arg (v) *sin|-----------------------------------------------------------------------------|| | 4 / |297 + 96*log(|v|) + log|----------------------------------|| + 9216*arg (v) *cos|-----------------------------------------------------------------------------| I*4 / |297 + 96*log(|v|) + log|----------------------------------|| + 9216*arg (v) *sin|-----------------------------------------------------------------------------|| |3 \/ \ \2111377674535255285545615254209921// \ 2 / \/ \ \2111377674535255285545615254209921// \ 2 /| |3 \/ \ \2111377674535255285545615254209921// \ 2 / \/ \ \2111377674535255285545615254209921// \ 2 /| |-- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|-- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \32 32 32 / \32 32 32 /
$$\left(- \frac{i \sqrt[4]{\left(96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297\right)^{2} + 9216 \arg^{2}{\left(v \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(96 \arg{\left(v \right)},96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297 \right)}}{2} \right)}}{32} - \frac{\sqrt[4]{\left(96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297\right)^{2} + 9216 \arg^{2}{\left(v \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(96 \arg{\left(v \right)},96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297 \right)}}{2} \right)}}{32} + \frac{3}{32}\right) \left(\frac{i \sqrt[4]{\left(96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297\right)^{2} + 9216 \arg^{2}{\left(v \right)}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(96 \arg{\left(v \right)},96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297 \right)}}{2} \right)}}{32} + \frac{\sqrt[4]{\left(96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297\right)^{2} + 9216 \arg^{2}{\left(v \right)}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(96 \arg{\left(v \right)},96 \log{\left(\left|{v}\right| \right)} + \log{\left(\frac{79228162514264337593543950336}{2111377674535255285545615254209921} \right)} + 297 \right)}}{2} \right)}}{32} + \frac{3}{32}\right)$$
=
9 3*log(2) 3*log(|v|) log(11) 3*I*arg(v) - -- - -------- - ---------- + ------- - ---------- 32 32 32 32 32
$$- \frac{3 \log{\left(\left|{v}\right| \right)}}{32} - \frac{3 i \arg{\left(v \right)}}{32} - \frac{9}{32} - \frac{3 \log{\left(2 \right)}}{32} + \frac{\log{\left(11 \right)}}{32}$$
-9/32 - 3*log(2)/32 - 3*log(|v|)/32 + log(11)/32 - 3*i*arg(v)/32