4a2=2a+3 ayudeme a resolverlo en formula general el 2 que esta alado del 4 es elevado al cuadradado
Respuestas
Respuesta dada por:
39
4a2=2a+3 ayudeme a resolverlo en formula general el 2 que esta a lado del 4 es elevado al cuadrado
![4a^2= 2a+3 \\ \\ 4a^2 - 2a-3 = 0\qquad igualamos \ a \ cero \\ \\ x_{1\ y\ 2}= \dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\qquad a= 4\qquad b=-2\qquad c= -3 \\ \\ \\ x_{1\ y\ 2}= \dfrac{-(-2)\pm \sqrt{(-2)^2-4(4)(-3)} }{2(4)} \\ \\ \\ x_{1\ y\ 2}= \dfrac{+2\pm \sqrt{4+ 48} }{8} \\ \\ \\ x_{1\ y\ 2}= \dfrac{+2\pm \sqrt{52} }{8} \\ \\ \\ x_{1\ y\ 2}= \dfrac{+2\pm 7,21 }{8} \\ \\ \\ x_{1}= \dfrac{+2+ 7,21 }{8}\qquad \qquad x_{ 2}= \dfrac{+2- 7,21 }{8} 4a^2= 2a+3 \\ \\ 4a^2 - 2a-3 = 0\qquad igualamos \ a \ cero \\ \\ x_{1\ y\ 2}= \dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\qquad a= 4\qquad b=-2\qquad c= -3 \\ \\ \\ x_{1\ y\ 2}= \dfrac{-(-2)\pm \sqrt{(-2)^2-4(4)(-3)} }{2(4)} \\ \\ \\ x_{1\ y\ 2}= \dfrac{+2\pm \sqrt{4+ 48} }{8} \\ \\ \\ x_{1\ y\ 2}= \dfrac{+2\pm \sqrt{52} }{8} \\ \\ \\ x_{1\ y\ 2}= \dfrac{+2\pm 7,21 }{8} \\ \\ \\ x_{1}= \dfrac{+2+ 7,21 }{8}\qquad \qquad x_{ 2}= \dfrac{+2- 7,21 }{8}](https://tex.z-dn.net/?f=4a%5E2%3D+2a%2B3+%5C%5C++%5C%5C+4a%5E2+-+2a-3+%3D+0%5Cqquad+igualamos+%5C+a+%5C+cero+%5C%5C++%5C%5C+x_%7B1%5C+y%5C+2%7D%3D+++%5Cdfrac%7B-b%5Cpm+%5Csqrt%7Bb%5E2-4ac%7D+%7D%7B2a%7D%5Cqquad+a%3D+4%5Cqquad+b%3D-2%5Cqquad+c%3D+-3+%5C%5C++%5C%5C++++%5C%5C+x_%7B1%5C+y%5C+2%7D%3D+++%5Cdfrac%7B-%28-2%29%5Cpm+%5Csqrt%7B%28-2%29%5E2-4%284%29%28-3%29%7D+%7D%7B2%284%29%7D++%5C%5C++%5C%5C+%5C%5C+x_%7B1%5C+y%5C+2%7D%3D+++%5Cdfrac%7B%2B2%5Cpm+%5Csqrt%7B4%2B+48%7D+%7D%7B8%7D+%5C%5C++%5C%5C++++%5C%5C+x_%7B1%5C+y%5C+2%7D%3D+++%5Cdfrac%7B%2B2%5Cpm+%5Csqrt%7B52%7D+%7D%7B8%7D+%5C%5C++%5C%5C+%5C%5C+x_%7B1%5C+y%5C+2%7D%3D+++%5Cdfrac%7B%2B2%5Cpm+7%2C21+%7D%7B8%7D+%5C%5C++%5C%5C+%5C%5C+x_%7B1%7D%3D+++%5Cdfrac%7B%2B2%2B+7%2C21+%7D%7B8%7D%5Cqquad+%5Cqquad++x_%7B+2%7D%3D+++%5Cdfrac%7B%2B2-+7%2C21+%7D%7B8%7D)
![x_{1}= \dfrac{9,21 }{8}\qquad \qquad x_{ 2}= \dfrac{-5,21 }{8}\\ \\ \\ x_{1}= \boxed{1,15 }\qquad \qquad x_{ 2}= \boxed{- 0,65 } x_{1}= \dfrac{9,21 }{8}\qquad \qquad x_{ 2}= \dfrac{-5,21 }{8}\\ \\ \\ x_{1}= \boxed{1,15 }\qquad \qquad x_{ 2}= \boxed{- 0,65 }](https://tex.z-dn.net/?f=+x_%7B1%7D%3D+++%5Cdfrac%7B9%2C21+%7D%7B8%7D%5Cqquad+%5Cqquad++x_%7B+2%7D%3D+++%5Cdfrac%7B-5%2C21+%7D%7B8%7D%5C%5C++%5C%5C+%5C%5C+x_%7B1%7D%3D+++%5Cboxed%7B1%2C15+%7D%5Cqquad+%5Cqquad++x_%7B+2%7D%3D+++%5Cboxed%7B-+0%2C65+%7D)
Espero que te sirva, salu2!!!!
Espero que te sirva, salu2!!!!
Respuesta dada por:
11
Resolverlo en formula general : 4a²=2a+3
![4a ^{2} =2a+3 4a ^{2} =2a+3](https://tex.z-dn.net/?f=4a+%5E%7B2%7D+%3D2a%2B3)
![4a^2-3=2a+3-3
4a^2-3=2a
4a^2-3-2a=2a-2a
4a^2-2a-3=0 4a^2-3=2a+3-3
4a^2-3=2a
4a^2-3-2a=2a-2a
4a^2-2a-3=0](https://tex.z-dn.net/?f=4a%5E2-3%3D2a%2B3-3%0A%0A4a%5E2-3%3D2a%0A%0A4a%5E2-3-2a%3D2a-2a%0A%0A4a%5E2-2a-3%3D0)
![ax^2+bx+c=0 ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
![\boxed{x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}} \boxed{x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}}](https://tex.z-dn.net/?f=%5Cboxed%7Bx_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-b%5Cpm+%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%7D%7D)
![\mathrm{Para\:}\quad a=4,\:b=-2,\:c=-3:\quad a_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:4\left(-3\right)}}{2\cdot \:4} \mathrm{Para\:}\quad a=4,\:b=-2,\:c=-3:\quad a_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:4\left(-3\right)}}{2\cdot \:4}](https://tex.z-dn.net/?f=%5Cmathrm%7BPara%5C%3A%7D%5Cquad+a%3D4%2C%5C%3Ab%3D-2%2C%5C%3Ac%3D-3%3A%5Cquad+a_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-%5Cleft%28-2%5Cright%29%5Cpm+%5Csqrt%7B%5Cleft%28-2%5Cright%29%5E2-4%5Ccdot+%5C%3A4%5Cleft%28-3%5Cright%29%7D%7D%7B2%5Ccdot+%5C%3A4%7D)
![a1= \frac{-\left(-2\right)+\sqrt{\left(-2\right)^2-4\cdot \:4\left(-3\right)}}{2\cdot \:4} a1= \frac{-\left(-2\right)+\sqrt{\left(-2\right)^2-4\cdot \:4\left(-3\right)}}{2\cdot \:4}](https://tex.z-dn.net/?f=a1%3D+%5Cfrac%7B-%5Cleft%28-2%5Cright%29%2B%5Csqrt%7B%5Cleft%28-2%5Cright%29%5E2-4%5Ccdot+%5C%3A4%5Cleft%28-3%5Cright%29%7D%7D%7B2%5Ccdot+%5C%3A4%7D)
![a1=\frac{2+\sqrt{52}}{8} a1=\frac{2+\sqrt{52}}{8}](https://tex.z-dn.net/?f=a1%3D%5Cfrac%7B2%2B%5Csqrt%7B52%7D%7D%7B8%7D)
![a1=\frac{2+2\sqrt{13}}{8} a1=\frac{2+2\sqrt{13}}{8}](https://tex.z-dn.net/?f=a1%3D%5Cfrac%7B2%2B2%5Csqrt%7B13%7D%7D%7B8%7D)
![a1=\frac{1+\sqrt{13}}{4} a1=\frac{1+\sqrt{13}}{4}](https://tex.z-dn.net/?f=a1%3D%5Cfrac%7B1%2B%5Csqrt%7B13%7D%7D%7B4%7D)
![a1=1.15139 a1=1.15139](https://tex.z-dn.net/?f=a1%3D1.15139)
![a2=\frac{2-\sqrt{\left(-2\right)^2-4\cdot \:4\left(-3\right)}}{2\cdot \:4} a2=\frac{2-\sqrt{\left(-2\right)^2-4\cdot \:4\left(-3\right)}}{2\cdot \:4}](https://tex.z-dn.net/?f=a2%3D%5Cfrac%7B2-%5Csqrt%7B%5Cleft%28-2%5Cright%29%5E2-4%5Ccdot+%5C%3A4%5Cleft%28-3%5Cright%29%7D%7D%7B2%5Ccdot+%5C%3A4%7D)
![a2=\frac{2-\sqrt{\left(-2\right)^2-\left(-3\right)\cdot \:4\cdot \:4}}{8} a2=\frac{2-\sqrt{\left(-2\right)^2-\left(-3\right)\cdot \:4\cdot \:4}}{8}](https://tex.z-dn.net/?f=a2%3D%5Cfrac%7B2-%5Csqrt%7B%5Cleft%28-2%5Cright%29%5E2-%5Cleft%28-3%5Cright%29%5Ccdot+%5C%3A4%5Ccdot+%5C%3A4%7D%7D%7B8%7D)
![a2=\frac{2-\sqrt{52}}{8} a2=\frac{2-\sqrt{52}}{8}](https://tex.z-dn.net/?f=a2%3D%5Cfrac%7B2-%5Csqrt%7B52%7D%7D%7B8%7D)
![a2=\frac{2-2\sqrt{13}}{8} a2=\frac{2-2\sqrt{13}}{8}](https://tex.z-dn.net/?f=a2%3D%5Cfrac%7B2-2%5Csqrt%7B13%7D%7D%7B8%7D)
![a2=\frac{2\left(1-\sqrt{13}\right)}{8} a2=\frac{2\left(1-\sqrt{13}\right)}{8}](https://tex.z-dn.net/?f=a2%3D%5Cfrac%7B2%5Cleft%281-%5Csqrt%7B13%7D%5Cright%29%7D%7B8%7D)
![a2=\frac{1-\sqrt{13}}{4} a2=\frac{1-\sqrt{13}}{4}](https://tex.z-dn.net/?f=a2%3D%5Cfrac%7B1-%5Csqrt%7B13%7D%7D%7B4%7D)
![a2=-0.65139 a2=-0.65139](https://tex.z-dn.net/?f=a2%3D-0.65139)
RESPUESTA :![\boxed{a_{1}=\frac{1+\sqrt{13}}{4},\:a_{2}=\frac{1-\sqrt{13}}{4}}} \boxed{a_{1}=\frac{1+\sqrt{13}}{4},\:a_{2}=\frac{1-\sqrt{13}}{4}}}](https://tex.z-dn.net/?f=%5Cboxed%7Ba_%7B1%7D%3D%5Cfrac%7B1%2B%5Csqrt%7B13%7D%7D%7B4%7D%2C%5C%3Aa_%7B2%7D%3D%5Cfrac%7B1-%5Csqrt%7B13%7D%7D%7B4%7D%7D%7D++)
En decimal :
![\boxed{a_{1}=1.15139\:\quad a_{2}=-0.65139}} \boxed{a_{1}=1.15139\:\quad a_{2}=-0.65139}}](https://tex.z-dn.net/?f=%5Cboxed%7Ba_%7B1%7D%3D1.15139%5C%3A%5Cquad+a_%7B2%7D%3D-0.65139%7D%7D)
RESPUESTA :
En decimal :
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