Question

1) Resolva as equações do 2º grau em R: a) x² + 3 = 4x
b) x² + x = 8x - 12
c) x(x - 2) = 2(x + 6)
​

Answer 1

$a) x^2+3=4x\\\\x^2+3-4x=4x-4x\\\\x^2-4x+3=0\\\\x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}\\\\x_{1,\:2}=\frac{-\left(-4\right)\pm \:2}{2\cdot \:1}\\\\x_1=\frac{-\left(-4\right)+2}{2\cdot \:1},\:x_2=\frac{-\left(-4\right)-2}{2\cdot \:1}\\\\x=3,\:x=1$                          

------------

$b)x^2+x=8x-12\\\\x^2+x+12=8x-12+12\\\\x^2+x+12=8x\\\\x^2+x+12-8x=8x-8x\\\\x^2-7x+12=0\\\\x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{\left(-7\right)^2-4\cdot \:1\cdot \:12}}{2\cdot \:1}\\\\x_{1,\:2}=\frac{-\left(-7\right)\pm \:1}{2\cdot \:1}\\\\x_1=\frac{-\left(-7\right)+1}{2\cdot \:1},\:x_2=\frac{-\left(-7\right)-1}{2\cdot \:1}\\\\x=4,\:x=3$

------------

$c)x\left(x-2\right)=2\left(x+6\right)\\\\x^2-2x=2x+12\\\\x^2-2x-12=2x+12-12\\\\x^2-2x-12=2x\\\\x^2-2x-12-2x=2x-2x\\\\x^2-4x-12=0\\\\x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\cdot \left(-12\right)}}{2\cdot \:1}\\\\x_{1,\:2}=\frac{-\left(-4\right)\pm \:8}{2\cdot \:1}\\\\x_1=\frac{-\left(-4\right)+8}{2\cdot \:1},\:x_2=\frac{-\left(-4\right)-8}{2\cdot \:1}\\\\x=6,\:x=-2$