Question

 o conjunto dos números reais, determinar o valor verdade  da proposições

a) (∃x) (2x = x)
b) (∃x) (x2 + 3x = −2) 

Answer 1

a)

2x=x
2x-x=0
x=0

b)

$x^{2} +3x=-2\\ \\ x^{2} +3x+2=0\\ \\ \Delta=3^2-4.1.2=9-8=1\\ \\ x=\frac{-3\pm1}{2}\\ \\ x_1=-1\\ \\ x_2=-2$

Answer 2

a) $2x=x$

$2x-x=0$

$\boxed{x=0}$

b) $x^2+3x=-2$

$x^2+3x+2=0$

$\Delta=3^2-4\cdot1\cdot2=9-8=1$

$x=\dfrac{-3\pm\sqrt{1}}{2\cdot1}=\dfrac{-3\pm1}{2}$

$x'=\dfrac{-3+1}{2}~\Rightarrow~\boxed{x'=-1}$

$x"=\dfrac{-3-1}{2}~\Rightarrow~\boxed{x"=-2}$