[tex]\displaystyle\\a^2=bc\Longleftrightarrow b=\frac{a^2}{c},~\textnormal{inlocuim in a doua relatie}, \left(\frac{a^2}{c}\right)^2=ac\Longleftrightarrow \\\frac{a^4}{c^2}=ac\Longleftrightarrow a^4=ac^3 \Longleftrightarrow a^3=c^3\Longleftrightarrow \boxed{a=c}~(1).\\a=c \Longrightarrow a^2=ab\Longleftrightarrow \boxed{a=b}~(2).\\\stackrel{(1),(2)}\Longrightarrow \boxed{a=b=c\implies triunghiul~este~echilateral.}[/tex]
