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- La ecuación:
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Ecuación x^3=4x^2+5x
-
Ecuación x^2=8x
-
Ecuación x^2=-x+6
-
Ecuación x^4-8*x^2+3=0
- Expresar {x} en función de y en la ecuación:
- -8*x-6*y=-20
- -20*x+1*y=12
- -6*x-8*y=18
- -11*x-18*y=18
-
Expresiones idénticas
- uno -a-(a/sqrt(uno -y^ dos))= cero
- 1 menos a menos (a dividir por raíz cuadrada de (1 menos y al cuadrado )) es igual a 0
- uno menos a menos (a dividir por raíz cuadrada de (uno menos y en el grado dos)) es igual a cero
- 1-a-(a/√(1-y^2))=0
- 1-a-(a/sqrt(1-y2))=0
- 1-a-a/sqrt1-y2=0
- 1-a-(a/sqrt(1-y²))=0
- 1-a-(a/sqrt(1-y en el grado 2))=0
- 1-a-a/sqrt1-y^2=0
- 1-a-(a/sqrt(1-y^2))=O
- 1-a-(a dividir por sqrt(1-y^2))=0
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Expresiones semejantes
- 1-a+(a/sqrt(1-y^2))=0
- 1-a-(a/sqrt(1+y^2))=0
- 1+a-(a/sqrt(1-y^2))=0
1-a-(a/sqrt(1-y^2))=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
a
1 - a - ----------- = 0
________
/ 2
\/ 1 - y
$$- \frac{a}{\sqrt{1 - y^{2}}} + \left(1 - a\right) = 0$$
Gráfica
Suma y producto de raíces
[src]
suma
/ / / 2 \ / 2 \\\ / / / 2 \ / 2 \\\ / / / 2 \ / 2 \\\ / / / 2 \ / 2 \\\
_______________________________________ | | | a | | a ||| _______________________________________ | | | a | | a ||| _______________________________________ | | | a | | a ||| _______________________________________ | | | a | | a |||
/ 2 |atan2|-im|---------|, 1 - re|---------||| / 2 |atan2|-im|---------|, 1 - re|---------||| / 2 |atan2|-im|---------|, 1 - re|---------||| / 2 |atan2|-im|---------|, 1 - re|---------|||
/ / / 2 \\ / 2 \ | | | 2| | 2||| / / / 2 \\ / 2 \ | | | 2| | 2||| / / / 2 \\ / 2 \ | | | 2| | 2||| / / / 2 \\ / 2 \ | | | 2| | 2|||
/ | | a || 2| a | | \ \(-1 + a) / \(-1 + a) //| / | | a || 2| a | | \ \(-1 + a) / \(-1 + a) //| / | | a || 2| a | | \ \(-1 + a) / \(-1 + a) //| / | | a || 2| a | | \ \(-1 + a) / \(-1 + a) //|
- / |1 - re|---------|| + im |---------| *cos|----------------------------------------| - I* / |1 - re|---------|| + im |---------| *sin|----------------------------------------| + / |1 - re|---------|| + im |---------| *cos|----------------------------------------| + I* / |1 - re|---------|| + im |---------| *sin|----------------------------------------|
4 / | | 2|| | 2| \ 2 / 4 / | | 2|| | 2| \ 2 / 4 / | | 2|| | 2| \ 2 / 4 / | | 2|| | 2| \ 2 /
\/ \ \(-1 + a) // \(-1 + a) / \/ \ \(-1 + a) // \(-1 + a) / \/ \ \(-1 + a) // \(-1 + a) / \/ \ \(-1 + a) // \(-1 + a) /
$$\left(- i \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} - \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ / / / 2 \ / 2 \\\ / / / 2 \ / 2 \\\\ / / / / 2 \ / 2 \\\ / / / 2 \ / 2 \\\\ | _______________________________________ | | | a | | a ||| _______________________________________ | | | a | | a |||| | _______________________________________ | | | a | | a ||| _______________________________________ | | | a | | a |||| | / 2 |atan2|-im|---------|, 1 - re|---------||| / 2 |atan2|-im|---------|, 1 - re|---------|||| | / 2 |atan2|-im|---------|, 1 - re|---------||| / 2 |atan2|-im|---------|, 1 - re|---------|||| | / / / 2 \\ / 2 \ | | | 2| | 2||| / / / 2 \\ / 2 \ | | | 2| | 2|||| | / / / 2 \\ / 2 \ | | | 2| | 2||| / / / 2 \\ / 2 \ | | | 2| | 2|||| | / | | a || 2| a | | \ \(-1 + a) / \(-1 + a) //| / | | a || 2| a | | \ \(-1 + a) / \(-1 + a) //|| | / | | a || 2| a | | \ \(-1 + a) / \(-1 + a) //| / | | a || 2| a | | \ \(-1 + a) / \(-1 + a) //|| |- / |1 - re|---------|| + im |---------| *cos|----------------------------------------| - I* / |1 - re|---------|| + im |---------| *sin|----------------------------------------||*| / |1 - re|---------|| + im |---------| *cos|----------------------------------------| + I* / |1 - re|---------|| + im |---------| *sin|----------------------------------------|| | 4 / | | 2|| | 2| \ 2 / 4 / | | 2|| | 2| \ 2 /| |4 / | | 2|| | 2| \ 2 / 4 / | | 2|| | 2| \ 2 /| \ \/ \ \(-1 + a) // \(-1 + a) / \/ \ \(-1 + a) // \(-1 + a) / / \\/ \ \(-1 + a) // \(-1 + a) / \/ \ \(-1 + a) // \(-1 + a) / /
$$\left(- i \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} - \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)}\right)$$
=
/ / 2 \ / 2 \\
________________________________________ | | a | | a ||
/ 2 I*atan2|-im|---------|, 1 - re|---------||
/ / / 2 \\ / 2 \ | | 2| | 2||
/ | | a || 2| a | \ \(-1 + a) / \(-1 + a) //
- / |-1 + re|---------|| + im |---------| *e
/ | | 2|| | 2|
\/ \ \(-1 + a) // \(-1 + a) /
$$- \sqrt{\left(\operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}$$
-sqrt((-1 + re(a^2/(-1 + a)^2))^2 + im(a^2/(-1 + a)^2)^2)*exp(i*atan2(-im(a^2/(-1 + a)^2), 1 - re(a^2/(-1 + a)^2)))
Respuesta rápida
[src]
/ / / 2 \ / 2 \\\ / / / 2 \ / 2 \\\
_______________________________________ | | | a | | a ||| _______________________________________ | | | a | | a |||
/ 2 |atan2|-im|---------|, 1 - re|---------||| / 2 |atan2|-im|---------|, 1 - re|---------|||
/ / / 2 \\ / 2 \ | | | 2| | 2||| / / / 2 \\ / 2 \ | | | 2| | 2|||
/ | | a || 2| a | | \ \(-1 + a) / \(-1 + a) //| / | | a || 2| a | | \ \(-1 + a) / \(-1 + a) //|
y1 = - / |1 - re|---------|| + im |---------| *cos|----------------------------------------| - I* / |1 - re|---------|| + im |---------| *sin|----------------------------------------|
4 / | | 2|| | 2| \ 2 / 4 / | | 2|| | 2| \ 2 /
\/ \ \(-1 + a) // \(-1 + a) / \/ \ \(-1 + a) // \(-1 + a) /
$$y_{1} = - i \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} - \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)}$$
/ / / 2 \ / 2 \\\ / / / 2 \ / 2 \\\
_______________________________________ | | | a | | a ||| _______________________________________ | | | a | | a |||
/ 2 |atan2|-im|---------|, 1 - re|---------||| / 2 |atan2|-im|---------|, 1 - re|---------|||
/ / / 2 \\ / 2 \ | | | 2| | 2||| / / / 2 \\ / 2 \ | | | 2| | 2|||
/ | | a || 2| a | | \ \(-1 + a) / \(-1 + a) //| / | | a || 2| a | | \ \(-1 + a) / \(-1 + a) //|
y2 = / |1 - re|---------|| + im |---------| *cos|----------------------------------------| + I* / |1 - re|---------|| + im |---------| *sin|----------------------------------------|
4 / | | 2|| | 2| \ 2 / 4 / | | 2|| | 2| \ 2 /
\/ \ \(-1 + a) // \(-1 + a) / \/ \ \(-1 + a) // \(-1 + a) /
$$y_{2} = i \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)} + \sqrt[4]{\left(1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2} + \left(\operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)},1 - \operatorname{re}{\left(\frac{a^{2}}{\left(a - 1\right)^{2}}\right)} \right)}}{2} \right)}$$
y2 = i*((1 - re(a^2/(a - 1)^2))^2 + im(a^2/(a - 1)^2)^2)^(1/4)*sin(atan2(-im(a^2/(a - 1)^2, 1 - re(a^2/(a - 1)^2))/2) + ((1 - re(a^2/(a - 1)^2))^2 + im(a^2/(a - 1)^2)^2)^(1/4)*cos(atan2(-im(a^2/(a - 1)^2), 1 - re(a^2/(a - 1)^2))/2))