[tex]\displaystyle\it\\pentru~ca~numerele~a,b,c~sunt~in~progresie~geometrica~rezulta~ca\\\boxed{b=\sqrt{ac}},~asadar~inlocuim~ce~am~obtinut~din~aceasta~informatie.\\-----------------------------\\(a+c)(b+c)(b^2+c^2-bc)=ab^3+ac^3+b^3c+c^4.\\(b^2+c^2)(ab+c^2)=ab^3+b^2c^2+abc^2+c^4,egalam.\\ab^3+ac^3+b^3c+c^4=ab^3+b^2c^2+abc^2+c^4,~\\reducem~termenii:ac^3+b^3c=b^2c^2+abc^2,~inlocuim.\\ac^3+ac^2\sqrt{ac}=ac^3+ac^2\sqrt{ac},~evident~adevarat.\\[/tex]
[tex]\displaystyle\it\\asadar,~cand~trei~numere~sunt~in~progresie~geometrica,\\are~loc~aceasta~egalitate.[/tex]