Answer to Question #231453 in Real Analysis for werd

Question

Find the infimum and supremum of {x ∈ R : x²+2x=3}

Answer 1

$\{x ∈ R : x^2+2x=3\}=\{x ∈ R : (x+1)^2=4\}=\{1, -3\}$

Therefore, $\inf \{x ∈ R : x^2+2x=3\}=\inf\{1, -3\}=-3$,

$\sup \{x ∈ R : x^2+2x=3\}=\sup\{1, -3\}=1$