 Probando LaTeX |
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 Jul 26 2008, 02:21 PM
Publicado:
#2371
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 Doctor en Matemáticas  Grupo: Usuario FMAT Mensajes: 176 Registrado: 4-June 08 Desde: Castro >> Conce Miembro Nº: 25.926 Nacionalidad:  Colegio/Liceo:  Universidad:  Sexo:   |
![TEX: \noindent $\boxed{P3}$\\<br />\begin{align}<br />\nonumber \dfrac{1-(x-y)^2}{1+x-y} &= \text{?}\\<br />\nonumber \\<br />\dfrac{1-(x-y)^2}{1+x-y} &= \dfrac{1-(x-y)^2}{1+x-y} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{/Factorizando}\\<br />\nonumber \\<br />\dfrac{1-(x-y)^2}{1+x-y} &= \dfrac{[1+(x-y)][1-(x-y)]}{1+x-y} \ \ \text{/Simplificamos}\\<br />\nonumber \\<br />\dfrac{1-(x-y)^2}{1+x-y} &= 1-(x+y) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{/Desarrollando el paréntesis}\\<br />\nonumber \\<br />\dfrac{1-(x-y)^2}{1+x-y} &= 1-x+y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{/Ordenando}\\<br />\nonumber \\<br />\dfrac{1-(x-y)^2}{1+x-y} &= 1+y-x<br />\end{align} \\ \\<br /><br />\noindent \boxed{Alternativa{\text{ }}E}<br />](./tex/062e53315aaa70136e4cef45c2f0f458.png)
Mensaje modificado por Kajoel el Jul 26 2008, 04:25 PM -------------------- |
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Jul 26 2008, 03:18 PM
Publicado:
#2372
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Maestro Matemático Grupo: Usuario FMAT Mensajes: 115 Registrado: 20-May 08 Miembro Nº: 23.908 Nacionalidad: Colegio/Liceo:  Universidad:  Sexo: |
![TEX: $\begin{gathered}<br /> P.2 \hfill \\<br /> \frac{a}<br />{b} + \frac{b}<br />{c} + \frac{c}<br />{a} = 1{\text{ Y }}abc = 3 \hfill \\<br /> entonces:{\text{ desarrollamos: }}\frac{a}<br />{b} + \frac{b}<br />{c} + \frac{c}<br />{a} = 1{\text{ }}\xrightarrow[{}]{{}}{\text{ }}\frac{{ab^2 + bc^2 + ca^2 }}<br />{{abc}} = 1 \hfill \\<br /> {\text{Nos Piden }}ab^2 + bc^2 + ca^2 {\text{ entonces simplemente reemplazamos el denominador de la fraccion}} \hfill \\<br /> {\text{resultante que es }}abc = 3{\text{ porque el enunciado del problema nos da esta informacion}}{\text{. }} \hfill \\<br /> {\text{y simplemente multiplicamos}} \hfill \\<br /> {\text{cruzado y obtenemos : }} \hfill \\<br /> {\text{ }}ab^2 + bc^2 + ca^2 = 3{\text{ Alternativa A}} \hfill \\ <br />\end{gathered} $<br />](./tex/4648e6e3892ba361496f3fbc0ce9f943.png) -------------------- Estudiante de Segundo Año
Universidad Técnica Federico Santa María  |
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Jul 26 2008, 07:42 PM
Publicado:
#2373
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 Dios Matemático Grupo: Usuario FMAT Mensajes: 363 Registrado: 12-October 06 Miembro Nº: 2.478 Nacionalidad: Colegio/Liceo:  Universidad:  Sexo:  |
![TEX: \[<br />\begin{gathered}<br /> {\text{21}}{\text{.}} \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> \frac{{\text{2}}}<br />{{\text{x}}} + \frac{{\text{3}}}<br />{{\text{y}}} = 2 \hfill \\<br /> \frac{{\text{4}}}<br />{{{\text{x}}^{\text{2}} }} + \frac{{\text{9}}}<br />{{{\text{y}}^{\text{2}} }} = 2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> xy = ? \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> \left[ {\frac{{\text{2}}}<br />{{\text{x}}} + \frac{{\text{3}}}<br />{{\text{y}}} = 2} \right] \bullet xy \hfill \\<br /> \left[ {\frac{{\text{4}}}<br />{{{\text{x}}^{\text{2}} }} + \frac{{\text{9}}}<br />{{{\text{y}}^{\text{2}} }} = 2} \right] \bullet x^2 y^2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> 2y + 3x = 2xy \hfill \\<br /> 4{\text{y}}^{\text{2}} + 9x^2 = 3x^2 y^2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> 2y + 3x = 2xy\left( {} \right)^2 \hfill \\<br /> 4{\text{y}}^{\text{2}} + 9x^2 = 3x^2 y^2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> 4{\text{y}}^{\text{2}} + 12xy + 9x^2 = 4x^2 y^2 \hfill \\<br /> 4{\text{y}}^{\text{2}} + 9x^2 = 3x^2 y^2 \left[ {} \right] - \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> 4{\text{y}}^{\text{2}} + 12xy + 9x^2 = 4x^2 y^2 \hfill \\<br /> - 4{\text{y}}^{\text{2}} - 9x^2 = - 3x^2 y^2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> 4{\text{y}}^{\text{2}} + 12xy + 9x^2 - 4{\text{y}}^{\text{2}} - 9x^2 = 4x^2 y^2 - 3x^2 y^2 \hfill \\<br /> 12xy = x^2 y^2 \hfill \\<br /> 12 = \frac{{x^2 y^2 }}<br />{{xy}} \hfill \\<br /> 12 = xy \hfill \\<br /> {\text{Alternativa C}} \hfill \\ <br />\end{gathered} <br />\]](./tex/35c667c560ca1a72b7563a841d163fd8.png)
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Jul 26 2008, 07:45 PM
Publicado:
#2374
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Dios Matemático Grupo: Usuario FMAT Mensajes: 363 Registrado: 12-October 06 Miembro Nº: 2.478 Nacionalidad: Colegio/Liceo: Universidad: Sexo: |
![TEX: \[<br />\begin{gathered}<br /> {\text{21}}{\text{.}} \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> \frac{{\text{2}}}<br />{{\text{x}}} + \frac{{\text{3}}}<br />{{\text{y}}} = 2 \hfill \\<br /> \frac{{\text{4}}}<br />{{{\text{x}}^{\text{2}} }} + \frac{{\text{9}}}<br />{{{\text{y}}^{\text{2}} }} = 2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \hfill \\<br /> xy = ? \hfill \\<br /> \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> \left[ {\frac{{\text{2}}}<br />{{\text{x}}} + \frac{{\text{3}}}<br />{{\text{y}}} = 2} \right] \bullet xy \hfill \\<br /> \left[ {\frac{{\text{4}}}<br />{{{\text{x}}^{\text{2}} }} + \frac{{\text{9}}}<br />{{{\text{y}}^{\text{2}} }} = 2} \right] \bullet x^2 y^2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> 2y + 3x = 2xy \hfill \\<br /> 4{\text{y}}^{\text{2}} + 9x^2 = 3x^2 y^2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> 2y + 3x = 2xy\left( {} \right)^2 \hfill \\<br /> 4{\text{y}}^{\text{2}} + 9x^2 = 3x^2 y^2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> 4{\text{y}}^{\text{2}} + 12xy + 9x^2 = 4x^2 y^2 \hfill \\<br /> 4{\text{y}}^{\text{2}} + 9x^2 = 3x^2 y^2 \left[ {} \right] - \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> 4{\text{y}}^{\text{2}} + 12xy + 9x^2 = 4x^2 y^2 \hfill \\<br /> - 4{\text{y}}^{\text{2}} - 9x^2 = - 3x^2 y^2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> 4{\text{y}}^{\text{2}} + 12xy + 9x^2 - 4{\text{y}}^{\text{2}} - 9x^2 = 4x^2 y^2 - 3x^2 y^2 \hfill \\<br /> \hfill \\<br /> 12xy = x^2 y^2 \hfill \\<br /> 12 = \frac{{x^2 y^2 }}<br />{{xy}} \hfill \\<br /> 12 = xy \hfill \\<br /> {\text{Alternativa C}} \hfill \\ <br />\end{gathered} <br />\]](./tex/error.gif)
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Jul 26 2008, 07:46 PM
Publicado:
#2375
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Dios Matemático Grupo: Usuario FMAT Mensajes: 363 Registrado: 12-October 06 Miembro Nº: 2.478 Nacionalidad: Colegio/Liceo: Universidad: Sexo: |
![TEX: \[<br />\begin{gathered}<br /> {\text{21}}{\text{.}} \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> \frac{{\text{2}}}<br />{{\text{x}}} + \frac{{\text{3}}}<br />{{\text{y}}} = 2 \hfill \\<br /> \frac{{\text{4}}}<br />{{{\text{x}}^{\text{2}} }} + \frac{{\text{9}}}<br />{{{\text{y}}^{\text{2}} }} = 2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> xy = ? \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> \left[ {\frac{{\text{2}}}<br />{{\text{x}}} + \frac{{\text{3}}}<br />{{\text{y}}} = 2} \right] \bullet xy \hfill \\<br /> \left[ {\frac{{\text{4}}}<br />{{{\text{x}}^{\text{2}} }} + \frac{{\text{9}}}<br />{{{\text{y}}^{\text{2}} }} = 2} \right] \bullet x^2 y^2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> 2y + 3x = 2xy \hfill \\<br /> 4{\text{y}}^{\text{2}} + 9x^2 = 3x^2 y^2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> 2y + 3x = 2xy\left( {} \right)^2 \hfill \\<br /> 4{\text{y}}^{\text{2}} + 9x^2 = 3x^2 y^2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> 4{\text{y}}^{\text{2}} + 12xy + 9x^2 = 4x^2 y^2 \hfill \\<br /> 4{\text{y}}^{\text{2}} + 9x^2 = 3x^2 y^2 \left[ {} \right] - \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> \left. {\underline {\, <br /> \begin{gathered}<br /> 4{\text{y}}^{\text{2}} + 12xy + 9x^2 = 4x^2 y^2 \hfill \\<br /> - 4{\text{y}}^{\text{2}} - 9x^2 = - 3x^2 y^2 \hfill \\ <br />\end{gathered} \,}}\! \right| \hfill \\<br /> 4{\text{y}}^{\text{2}} + 12xy + 9x^2 - 4{\text{y}}^{\text{2}} - 9x^2 = 4x^2 y^2 - 3x^2 y^2 \hfill \\<br /> 12xy = x^2 y^2 \hfill \\<br /> 12 = \frac{{x^2 y^2 }}<br />{{xy}} \hfill \\<br /> 12 = xy \hfill \\<br /> {\text{Alternativa C}} \hfill \\ <br />\end{gathered} <br />\]](./tex/f3a0c7b56161b1a85c238230912da1ce.png)
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Jul 26 2008, 07:46 PM
Publicado:
#2376
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Dios Matemático Grupo: Usuario FMAT Mensajes: 363 Registrado: 12-October 06 Miembro Nº: 2.478 Nacionalidad: Colegio/Liceo: Universidad: Sexo: |
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Jul 26 2008, 07:48 PM
Publicado:
#2377
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Dios Matemático Grupo: Usuario FMAT Mensajes: 363 Registrado: 12-October 06 Miembro Nº: 2.478 Nacionalidad: Colegio/Liceo: Universidad: Sexo: |
![TEX: \[<br />\begin{gathered}<br /> {\text{15}}{\text{.}} \hfill \\<br /> {\text{f}}\left( {{\text{x + 1}}} \right) = x^2 \hfill \\<br /> f\left( 3 \right) = ? \hfill \\<br /> x + 1 = 3 \hfill \\<br /> x = 2 \hfill \\<br /> {\text{f}}\left( {\text{3}} \right) = \left( 2 \right)^2 \hfill \\<br /> {\text{f}}\left( {\text{3}} \right) = 4 \hfill \\<br /> Alternativa{\text{ B}} \hfill \\ <br />\end{gathered} <br />\]](./tex/5644dd525c799e9027e4b5d54dac88af.png)
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Jul 26 2008, 07:49 PM
Publicado:
#2378
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Dios Matemático Grupo: Usuario FMAT Mensajes: 363 Registrado: 12-October 06 Miembro Nº: 2.478 Nacionalidad: Colegio/Liceo: Universidad: Sexo: |
![TEX: \[<br />\begin{gathered}<br /> {\text{9}}{\text{.}} \hfill \\<br /> 3 - \frac{3}<br />{{3 - \frac{1}<br />{x}}} = 1 \hfill \\<br /> x = ? \hfill \\<br /> 3 - \frac{3}<br />{{\frac{{3x - 1}}<br />{x}}} = 1 \hfill \\<br /> 3 - \frac{{3x}}<br />{{3x - 1}} = 1 \hfill \\<br /> \left( {3x - 1} \right) \bullet 3 - \frac{{3x}}<br />{{3x - 1}} \bullet \left( {3x - 1} \right) = \left( {3x - 1} \right) \hfill \\<br /> 9x - 3 - 3x = 3x - 1 \hfill \\<br /> 3x = 2 \hfill \\<br /> x = \frac{2}<br />{3} \hfill \\<br /> {\text{Alternativa E}} \hfill \\ <br />\end{gathered} <br />\]](./tex/b42a55d55405e26a5d2da5943bfa5f7e.png) |
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Jul 26 2008, 07:50 PM
Publicado:
#2379
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Dios Matemático Grupo: Usuario FMAT Mensajes: 363 Registrado: 12-October 06 Miembro Nº: 2.478 Nacionalidad: Colegio/Liceo: Universidad: Sexo: |
![TEX: \[<br />\begin{gathered}<br /> {\text{6}}{\text{.}} \hfill \\<br /> {\text{a + b = 2008}} \hfill \\<br /> {\text{ab = 2008}} \hfill \\<br /> \frac{{{\text{a}}^{\text{2}} + b^2 }}<br />{{2008}} = ? \hfill \\<br /> {\text{Cuadrado de binomio}} \hfill \\<br /> \left( {{\text{a + b}}} \right)^2 = {\text{a}}^{\text{2}} + 2ab + b^2 \hfill \\<br /> \left( {{\text{2008}}} \right)^2 = {\text{a}}^{\text{2}} + 2 \bullet 2008 + b^2 \hfill \\<br /> \left( {{\text{2008}}} \right)^2 - \left( {2 \bullet 2008} \right) = {\text{a}}^{\text{2}} + b^2 \hfill \\<br /> \frac{{\left( {{\text{2008}}} \right)^2 - \left( {2 \bullet 2008} \right)}}<br />{{2008}} = \frac{{\left( {{\text{2008}}} \right)\left( {2008 - 2} \right)}}<br />{{2008}} = 2006 \hfill \\<br /> Alternativa{\text{ B}} \hfill \\ <br />\end{gathered} <br />\]](./tex/cdbfadab5e5ddb338300e817c32e9d32.png)
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Jul 26 2008, 07:50 PM
Publicado:
#2380
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Dios Matemático Grupo: Usuario FMAT Mensajes: 363 Registrado: 12-October 06 Miembro Nº: 2.478 Nacionalidad: Colegio/Liceo: Universidad: Sexo: |
![TEX: \[<br />\begin{gathered}<br /> 4. \hfill \\<br /> \left( {X - 37} \right)^2 - 169 = 0 \hfill \\<br /> {\text{Suma por diferencia}} \hfill \\<br /> \left( {{\text{X}} - 37 - 13} \right)\left( {{\text{X}} - 37 + 13} \right) \hfill \\<br /> \left( {{\text{X}} - 50} \right)\left( {{\text{X}} - 24} \right) = 0 \hfill \\<br /> X = 50{\text{ X = 24}} \hfill \\<br /> {\text{Alternativa D}} \hfill \\ <br />\end{gathered} <br />\]](./tex/5342203a5a67c6c83f9cd2388e9ca2d0.png)
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