Question

Ayudenme , Con Procedimiento
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Gracias (:

Answer 1

6. Las ecuaciones cuadráticas:

Resolvemos por la formula general:

$\boxed{ x=\dfrac{-b\pm \sqrt{b ^{2}-4ac } }{2a}}$

Necesitamos saber los siguientes datos:

a= 4
b= 9
c= 5

Resolvemos:

a) 4x²+9x+5= 0

$x=\dfrac{-9\pm \sqrt{(9) ^{2}-4(4)(5) } }{2(4)}} \\ \\ \\ x=\dfrac{-9\pm \sqrt{81-80 } }{8}} \\ \\ \\ x=\dfrac{-9\pm \sqrt{1 } }{8}} \\ \\ \\ x=\dfrac{-9\pm 1 }{8}} \\ \\ \\ x_{1} =\dfrac{-9+ 1 }{8}} \\ \\ \\ x_{1} =\dfrac{-8 }{8}} \\ \\ \boxed{\textbf{ x}_{1} \textbf{ = -1}}\checkmark\checkmark \\ \\ x_2=\dfrac{-9- 1 }{8}} \\ \\ \\ \textbf{x}_\textbf{{2}}\textbf{=}\textbf{-}\dfrac{ \not{\textbf{10} } }{\not{\textbf{8}}} \\ \\ Simplificamos usando a \textbf{2}:$

$\boxed{\textbf{x}_\textbf{{2}}\textbf{=}\textbf{-}\dfrac{\textbf{5} }{\textbf{4}} }\checkmark\checkmark$

b) 8m²+18m+9= 0.

Necesitamos saber los siguientes datos:

a= 8
b= 18
c= 9

$m=\dfrac{-18\pm \sqrt{(18) ^{2}-4(8)(9) } }{2(8)}} \\ \\ \\ m=\dfrac{-18\pm \sqrt{324-288 } }{16}} \\ \\ \\ m=\dfrac{-18/\pm \sqrt{36 } }{16}} \\ \\ \\ m=\dfrac{-18\pm 6 }{16}} \\ \\ \\ m_{1} =\dfrac{-18+ 6 }{16}} \\ \\ \\ m_{1} =\dfrac{-12 }{16}} \\ \\ Factorizamos usando a \textbf{4}: \\ \\\textbf{ m}_{1}= -\dfrac{\not4 \times 3}{\not4\times 4} \\ \\ \\ \boxed{\textbf{ m}_{\textbf{1}}= \textbf{-}\dfrac{ \textbf{3}}{ \textbf{4} }} \checkmark\checkmark$

$m_{2} =\dfrac{-18- 6 }{16}} \\ \\ \\ m_{2} =-\dfrac{24 }{16}} \\ \\ Factorizamos usando a \textbf{8}: \\ \\ m_{2} =-\dfrac{\not8 \times 3 }{\not8\times2}} \\ \\ \\ \boxed{\textbf{ m}_{2}= \textbf{-}\dfrac{ \textbf{3}}{ \textbf{2} }}} \checkmark\checkmark$

c) 6n²-13n+6= 0.

Necesitamos saber los siguientes datos:

a= 6
b= -13
c= 6

$n=\dfrac{-(-13)\pm \sqrt{(-13) ^{2}-4(6)(6) } }{2(6)}} \\ \\ \\ n=\dfrac{13\pm \sqrt{169-144 } }{12}} \\ \\ \\ n=\dfrac{13\pm \sqrt{25 } }{12}} \\ \\ \\ n=\dfrac{13\pm 5 }{12}} \\ \\ \\ n_{1} =\dfrac{13+ 5 }{12}} \\ \\ \\ \textbf{n}_{1}\textbf{=}\dfrac{\textbf{18}}{\textbf{12}} \\ \\ Factorizamos usando a \textbf{6}: \\ \\ \textbf{n}_{1}\textbf{=}\dfrac{\not\textbf{6} \times\textbf{{3}}}{\not\textbf{6} \times\textbf{2}}$

$\boxed{\textbf{n}_{1}\textbf{=}\dfrac{\textbf{{3}}}{\textbf{2}}}\checkmark\checkmark$

$n_2=\dfrac{13- 5 }{12}} \\ \\ \\ n_2=\dfrac{8}{12}} \\ \\ Factorizamos usando a \textbf{4} \\ \\ n_2= \dfrac{\not4 \times 2}{\not4 \times 3}} \\ \\ \\ \boxed{\textbf{n}_{2}\textbf{=}\dfrac{\textbf{{2}}}{\textbf{3}}}\checkmark\checkmark$

d) 15x²+4x-3= 0.

Necesitamos saber los siguientes datos:

a= 15
b= 4
c= -3

$x=\dfrac{-4\pm \sqrt{(4) ^{2}-4(15)(-3) } }{2(15)}} \\ \\ \\ x=\dfrac{-4\pm \sqrt{16+180 } }{30}} \\ \\ \\ x=\dfrac{-4\pm \sqrt{196 } }{30}} \\ \\ \\ x=\dfrac{-4\pm 14 }{30}} \\ \\ \\ x_1=\dfrac{-4+ 14 }{30}} \\ \\ \\ x_1=\dfrac{10 }{30}} \\ \\ Factorizamos usando a \textbf{10}:$

$\\ \\ x_1=\dfrac{\not10\times1 }{\not10\times3}} \\ \\ \\ \boxed{\textbf{x}_{1}\textbf{=}\dfrac{\textbf{{1}}}{\textbf{3}}}\checkmark\checkmark \\ \\ \\ x_2=\dfrac{-4-14 }{30}} \\ \\ \\ x_2=\dfrac{-18 }{30}}$

${ Factorizamos usando a \textbf{6}: \\ \\ \\ x_2=-\dfrac{\not6\times3 }{\not6\times5}} \\ \\ \\ \boxed{\textbf{x}_{2}\textbf{=-}\dfrac{\textbf{{3}}}{\textbf{5}}}\checkmark\checkmark$

Saludos y Suerte!!!!!!