Toán cho a^3-3ab^2=5 và b^3-3a^2b=10 tính a^2+b^2 28/08/2021 By Aubrey cho a^3-3ab^2=5 và b^3-3a^2b=10 tính a^2+b^2
NÈ a/(1+b²)=(a+ba²-ab²)/(1+b²)=(a(1+b²)-a…tuong tu: b/(1+c²)>=b-bc/2; c/(1+a²)>=c-ac/2.=> a/(1+b²)+b/(1+c²)+c/(1+a²)>=a+b+c-1/2(ab…ma: 3(ab+bc+ca)<=(a+b+c)²=9=> ab+bc+ca<=3=>-1/2(ab+bc+ca)>=-3/2=> a+b+c-1/2(ab+bc+ca)>=3-3/2=3/2=> a/(1+b²)+b/(1+c²)+c/(1+a²)>= 3/2(dpcm)dau “=” say ra <=> a=b=c=1 Trả lời
NÈ
a/(1+b²)=(a+ba²-ab²)/(1+b²)=(a(1+b²)-a…
tuong tu: b/(1+c²)>=b-bc/2; c/(1+a²)>=c-ac/2.
=> a/(1+b²)+b/(1+c²)+c/(1+a²)>=a+b+c-1/2(ab…
ma: 3(ab+bc+ca)<=(a+b+c)²=9=> ab+bc+ca<=3
=>-1/2(ab+bc+ca)>=-3/2
=> a+b+c-1/2(ab+bc+ca)>=3-3/2=3/2
=> a/(1+b²)+b/(1+c²)+c/(1+a²)>= 3/2(dpcm)
dau “=” say ra <=> a=b=c=1