Đáp án:
Giải thích các bước giải:
Do `a,b,c>=0` ,Áp dụng BĐT Co-si
`=>a+b+1>=3`$\sqrt[3]{a.b.1}$ `=3`$\sqrt[3]{ab}$
`=>a+c+1>=3`$\sqrt[3]{a.c.1}$ `=3`$\sqrt[3]{ac}$
`=>b+c+1>=3`$\sqrt[3]{b.c.1}$ `=3`$\sqrt[3]{bc}$
`=>(a+b+1)+(a+c+1)+(b+c+1)>=3`$\sqrt[3]{ab}$`+3`$\sqrt[3]{ac}$`+3`$\sqrt[3]{bc}$
`=>2(a+b+c)+3>=3(`$\sqrt[3]{ab}$`+`$\sqrt[3]{bc}$`+`$\sqrt[3]{ac}$`)`
`=>2/3 (a+b+c)+1>=`$\sqrt[3]{ab}$`+`$\sqrt[3]{bc}$`+`$\sqrt[3]{ac}$
Dấu`=` xảy ra `<=>a=b=c=1`