Wykaż, że jeżeli a+b=3 oraz ab=-28, to a³+b³ > 250

Zakładam: [latex]a+b=3\ ab=-28[/latex] Teza: [latex]a^3+b^3 extgreater 250[/latex] [latex]a+b=3\ (a+b)^3=27\ a^3+3a^2b+3ab^3+b^3=27\ a^3+3aab+3bab+b^3=27\ a^3+3a*(-28)+3b*(-28)+b^3=27\ a^3-84a-84b+b^3=27\ a^3+b^3-84(a+b)=27\ a^3+b^3-84*3=27\ a^3+b^3-252=27\ a^3+b^3=279\ 279 extgreater 250implies a^3+b^3 extgreater 250 cnd.[/latex]