Question

resolver las siguientes ecuaciones por el metodo que mas convenga
5x(x-)+21=6x+24
(3x-2)(x+1)=2
(2x)/(x-1)+(4)/(x+2)=5

Answer 1

Respuesta:

5x(x-)+21=6x+24

5x²+21=6x+24

5x²+21-6x-24=0

5x²-3-6x = 0

$x=\frac{6+4\sqrt{6}}{10}, x=\frac{6-4\sqrt{6}}{10}$

$x=\frac{3+2\sqrt{6}}{5},\:x=\frac{3-2\sqrt{6}}{5}$

Answer 2

Explicación paso a paso:

(3x-2)(x+1)=2

3x² + 3x - 2x -2 =2

3x² + x -2 -2=0

3x² + x -4=0

Donde:  

a = 3

b = 1

c = -4

 

Desarrollamos:  

$x_{1,\:2}=\frac{-\left(1\right)\pm \sqrt{\left(1\right)^2-4\cdot \:3\cdot \:-4}}{2\cdot \:3} \\\\ x_{1,\:2}=\frac{-1\pm \sqrt{1+48}}{6} \\\\ x_{1,\:2}=\frac{-1\pm \sqrt{49}}{6} \\\\ x_{1,\:2}=\frac{-1\pm7}{6}$

Separar las soluciones:  

$x_1=\frac{-1+7}{6},\:x_2=\frac{-1-7}{6} \\\\ x_1=\frac{6}{6},\:x_2=\frac{-8}{6} \\\\ x_1=1,\:x_2=\frac{-4}{3}$

(2x)/(x-1)+(4)/(x+2)=5

2x(x+2) + 4(x-1) = 5(x+2) (x-1)

2x² + 4x + 4x - 4 = 5(x²-x+2x-2)

2x² + 8x - 4 = 5(x²+x-2)

2x² + 8x - 4  = 5x² +5x - 10

2x²-5x² + 8x -5x - 4  +10 = 0

-3x² + 3x + 6 = 0

Donde:      

a = -3    

b = 3    

c = 6    

     

Desarrollamos:      

$x_{1,\:2}=\frac{-\left(3\right)\pm \sqrt{\left(3\right)^2-4\cdot \:-3\cdot \:6}}{2\cdot \:-3} \\\\ x_{1,\:2}=\frac{-3\pm \sqrt{9+72}}{-6} \\\\ x_{1,\:2}=\frac{-3\pm \sqrt{81}}{-6} \\\\ x_{1,\:2}=\frac{-3\pm9}{-6}$      

     

Separar las soluciones:      

$x_1=\frac{-3+9}{-6},\:x_2=\frac{-3-9}{-6} \\\\ x_1=\frac{6}{-6},\:x_2=\frac{-12}{-6} \\\\ x_1=-1,\:x_2=2$