Respuestas
Respuesta dada por:
139
La forma cuadrática :
ax² + bx + c.
x² + 11x + 24 = 0
Dónde :
a = 1
b = 11
c = 24
Fórmula cuadrática.
![\boxed{\boxed{ x_{1,2} = \frac{-b\ñ \sqrt{b^{2}-4ac}}{2a}}} \boxed{\boxed{ x_{1,2} = \frac{-b\ñ \sqrt{b^{2}-4ac}}{2a}}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B+x_%7B1%2C2%7D+%3D++%5Cfrac%7B-b%5C%C3%B1+%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D%7D%7D)
Reemplazamos :
![x_{1,2} = \dfrac{-11\ñ \sqrt{(11)^{2}-4(1)(24)}}{2(1)} \\ \\ \\ x_{1,2} = \dfrac{-11\ñ \sqrt{121-96}}{2} \\ \\ \\ x_{1,2} = \dfrac{-11\ñ \sqrt{25}}{2} \\ \\ \\ x_{1,2} = \dfrac{-11\ñ5}{2} \\ \\ Tenemos\ dos\ soluciones: \\ \\ x_{1}= \dfrac{11+5}{2} = \dfrac{16}{2} = 8 \\ \\ \\ x_{2} = \dfrac{11-5}{2} = \dfrac{6}{2} = 3 x_{1,2} = \dfrac{-11\ñ \sqrt{(11)^{2}-4(1)(24)}}{2(1)} \\ \\ \\ x_{1,2} = \dfrac{-11\ñ \sqrt{121-96}}{2} \\ \\ \\ x_{1,2} = \dfrac{-11\ñ \sqrt{25}}{2} \\ \\ \\ x_{1,2} = \dfrac{-11\ñ5}{2} \\ \\ Tenemos\ dos\ soluciones: \\ \\ x_{1}= \dfrac{11+5}{2} = \dfrac{16}{2} = 8 \\ \\ \\ x_{2} = \dfrac{11-5}{2} = \dfrac{6}{2} = 3](https://tex.z-dn.net/?f=+x_%7B1%2C2%7D+%3D+++%5Cdfrac%7B-11%5C%C3%B1+%5Csqrt%7B%2811%29%5E%7B2%7D-4%281%29%2824%29%7D%7D%7B2%281%29%7D+%5C%5C+%5C%5C+%5C%5C++x_%7B1%2C2%7D+%3D+%5Cdfrac%7B-11%5C%C3%B1+%5Csqrt%7B121-96%7D%7D%7B2%7D+%5C%5C+%5C%5C+%5C%5C+x_%7B1%2C2%7D+%3D+%5Cdfrac%7B-11%5C%C3%B1+%5Csqrt%7B25%7D%7D%7B2%7D+%5C%5C+%5C%5C+%5C%5C+++x_%7B1%2C2%7D+%3D++%5Cdfrac%7B-11%5C%C3%B15%7D%7B2%7D+%5C%5C+%5C%5C+Tenemos%5C+dos%5C+soluciones%3A+%5C%5C+%5C%5C++x_%7B1%7D%3D+%5Cdfrac%7B11%2B5%7D%7B2%7D+%3D++%5Cdfrac%7B16%7D%7B2%7D+%3D+8+%5C%5C+%5C%5C+%5C%5C++x_%7B2%7D+%3D+%5Cdfrac%7B11-5%7D%7B2%7D+%3D+%5Cdfrac%7B6%7D%7B2%7D+%3D+3++++++)
Solución :
8 y 3.
ax² + bx + c.
x² + 11x + 24 = 0
Dónde :
a = 1
b = 11
c = 24
Fórmula cuadrática.
Reemplazamos :
Solución :
8 y 3.
osvaldo28:
gracias
Respuesta dada por:
182
Resolvemos mediante la formula General:
![\boxed{\boxed{ \textbf{x = } \dfrac{\textbf{-b}\pm \sqrt{\textbf{b}^{\textbf{2}}\textbf{-4ac}}}{\textbf{2a}}}} \boxed{\boxed{ \textbf{x = } \dfrac{\textbf{-b}\pm \sqrt{\textbf{b}^{\textbf{2}}\textbf{-4ac}}}{\textbf{2a}}}}](https://tex.z-dn.net/?f=+%5Cboxed%7B%5Cboxed%7B+%5Ctextbf%7Bx+%3D+%7D+%5Cdfrac%7B%5Ctextbf%7B-b%7D%5Cpm+%5Csqrt%7B%5Ctextbf%7Bb%7D%5E%7B%5Ctextbf%7B2%7D%7D%5Ctextbf%7B-4ac%7D%7D%7D%7B%5Ctextbf%7B2a%7D%7D%7D%7D)
Donde:
a= 1
b= 11
c= 24.
![x^{2} +11x=-24 x^{2} +11x=-24](https://tex.z-dn.net/?f=+x%5E%7B2%7D+%2B11x%3D-24+)
Movemos a todos los datos a la izquierda:
![x^{2} +11x+24=0 x^{2} +11x+24=0](https://tex.z-dn.net/?f=+x%5E%7B2%7D+%2B11x%2B24%3D0)
Sustituimos datos y resolvemos:
![\textbf{x = } \dfrac{\textbf{-11}\pm \sqrt{\textbf{(11)}^{\textbf{2}}\textbf{-4(1)(24)}}}{\textbf{2(1)}} \\ \\ \\ \textbf{x = } \dfrac{\textbf{-11}\pm \sqrt{\textbf{121}\textbf{-96}}}{\textbf{2}} \\ \\ \\ \textbf{x = } \dfrac{\textbf{-11}\pm \sqrt{\textbf{25}}}{\textbf{2}} \\ \\ $Resolvemos la ra\'iz cuadrada: \textbf{x = } \dfrac{\textbf{-11}\pm \sqrt{\textbf{(11)}^{\textbf{2}}\textbf{-4(1)(24)}}}{\textbf{2(1)}} \\ \\ \\ \textbf{x = } \dfrac{\textbf{-11}\pm \sqrt{\textbf{121}\textbf{-96}}}{\textbf{2}} \\ \\ \\ \textbf{x = } \dfrac{\textbf{-11}\pm \sqrt{\textbf{25}}}{\textbf{2}} \\ \\ $Resolvemos la ra\'iz cuadrada:](https://tex.z-dn.net/?f=%5Ctextbf%7Bx+%3D+%7D+%5Cdfrac%7B%5Ctextbf%7B-11%7D%5Cpm+%5Csqrt%7B%5Ctextbf%7B%2811%29%7D%5E%7B%5Ctextbf%7B2%7D%7D%5Ctextbf%7B-4%281%29%2824%29%7D%7D%7D%7B%5Ctextbf%7B2%281%29%7D%7D+%5C%5C+%5C%5C+%5C%5C+%5Ctextbf%7Bx+%3D+%7D+%5Cdfrac%7B%5Ctextbf%7B-11%7D%5Cpm+%5Csqrt%7B%5Ctextbf%7B121%7D%5Ctextbf%7B-96%7D%7D%7D%7B%5Ctextbf%7B2%7D%7D+%5C%5C+%5C%5C+%5C%5C+%5Ctextbf%7Bx+%3D+%7D+%5Cdfrac%7B%5Ctextbf%7B-11%7D%5Cpm+%5Csqrt%7B%5Ctextbf%7B25%7D%7D%7D%7B%5Ctextbf%7B2%7D%7D+%5C%5C+%5C%5C+%24Resolvemos+la+ra%5C%27iz+cuadrada%3A)
![\textbf{x = } \dfrac{\textbf{-11}\pm\textbf{5}}{\textbf{2}} \\ \\ \\ \textbf{x}_ \textbf{1}} \textbf{ = } \dfrac{\textbf{-11}+\textbf{5}}{\textbf{2}}\Longleftarrow \boxed{\textbf{Primera ecuaci\'on}} \checkmark \\ \\ \\ \textbf{x}_ \textbf{1}} \textbf{ = } \dfrac{\textbf{-6}}{\textbf{2}} \\ \\ \boxed{\boxed{\textbf{x}_ \textbf{1} \textbf{ = -3}}}\checkmark\checkmark \textbf{x = } \dfrac{\textbf{-11}\pm\textbf{5}}{\textbf{2}} \\ \\ \\ \textbf{x}_ \textbf{1}} \textbf{ = } \dfrac{\textbf{-11}+\textbf{5}}{\textbf{2}}\Longleftarrow \boxed{\textbf{Primera ecuaci\'on}} \checkmark \\ \\ \\ \textbf{x}_ \textbf{1}} \textbf{ = } \dfrac{\textbf{-6}}{\textbf{2}} \\ \\ \boxed{\boxed{\textbf{x}_ \textbf{1} \textbf{ = -3}}}\checkmark\checkmark](https://tex.z-dn.net/?f=%5Ctextbf%7Bx+%3D+%7D+%5Cdfrac%7B%5Ctextbf%7B-11%7D%5Cpm%5Ctextbf%7B5%7D%7D%7B%5Ctextbf%7B2%7D%7D+%5C%5C+%5C%5C+%5C%5C+%5Ctextbf%7Bx%7D_+%5Ctextbf%7B1%7D%7D+%5Ctextbf%7B+%3D+%7D+%5Cdfrac%7B%5Ctextbf%7B-11%7D%2B%5Ctextbf%7B5%7D%7D%7B%5Ctextbf%7B2%7D%7D%5CLongleftarrow+%5Cboxed%7B%5Ctextbf%7BPrimera+ecuaci%5C%27on%7D%7D+%5Ccheckmark+++%5C%5C+%5C%5C+%5C%5C+%5Ctextbf%7Bx%7D_+%5Ctextbf%7B1%7D%7D+%5Ctextbf%7B+%3D+%7D+%5Cdfrac%7B%5Ctextbf%7B-6%7D%7D%7B%5Ctextbf%7B2%7D%7D+%5C%5C+%5C%5C+%5Cboxed%7B%5Cboxed%7B%5Ctextbf%7Bx%7D_+%5Ctextbf%7B1%7D+%5Ctextbf%7B+%3D+-3%7D%7D%7D%5Ccheckmark%5Ccheckmark)
![\textbf{x}_ \textbf{2}} \textbf{ = } \dfrac{\textbf{-11}-\textbf{5}}{\textbf{2}}\Longleftarrow \boxed{\textbf{Segunda ecuaci\'on}} \checkmark \\ \\ \\ \textbf{x}_ \textbf{2}} \textbf{ = } \dfrac{\textbf{-16}}{\textbf{2}} \\ \\ \boxed{\boxed{\textbf{x}_ \textbf{2} \textbf{ = -8}}}\checkmark\checkmark \textbf{x}_ \textbf{2}} \textbf{ = } \dfrac{\textbf{-11}-\textbf{5}}{\textbf{2}}\Longleftarrow \boxed{\textbf{Segunda ecuaci\'on}} \checkmark \\ \\ \\ \textbf{x}_ \textbf{2}} \textbf{ = } \dfrac{\textbf{-16}}{\textbf{2}} \\ \\ \boxed{\boxed{\textbf{x}_ \textbf{2} \textbf{ = -8}}}\checkmark\checkmark](https://tex.z-dn.net/?f=%5Ctextbf%7Bx%7D_+%5Ctextbf%7B2%7D%7D+%5Ctextbf%7B+%3D+%7D+%5Cdfrac%7B%5Ctextbf%7B-11%7D-%5Ctextbf%7B5%7D%7D%7B%5Ctextbf%7B2%7D%7D%5CLongleftarrow+%5Cboxed%7B%5Ctextbf%7BSegunda+ecuaci%5C%27on%7D%7D+%5Ccheckmark+%5C%5C++%5C%5C++%5C%5C+%5Ctextbf%7Bx%7D_+%5Ctextbf%7B2%7D%7D+%5Ctextbf%7B+%3D+%7D+%5Cdfrac%7B%5Ctextbf%7B-16%7D%7D%7B%5Ctextbf%7B2%7D%7D+%5C%5C++%5C%5C++%5Cboxed%7B%5Cboxed%7B%5Ctextbf%7Bx%7D_+%5Ctextbf%7B2%7D+%5Ctextbf%7B+%3D+-8%7D%7D%7D%5Ccheckmark%5Ccheckmark)
Saludos y Suerte!!!!!
Donde:
a= 1
b= 11
c= 24.
Movemos a todos los datos a la izquierda:
Sustituimos datos y resolvemos:
Saludos y Suerte!!!!!
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