`text{Xét tam giác ABC}`
`b+c>a(BĐT` $\Delta$)
`=>b+c-a>0`
`CMT^2:c+a-b>0,a+b-c>0`
`+)a/(b+c-a)=a^2/(ab+bc-a^2)`
`b/(a+c-b)=b^2/(ab+bc-b^2)`
`c/(a+b-c)=c^2/(ac+bc-c^2)`
`text{Áp dụng BĐT cauchy-swart ta có}`
`A>=(a+b+c)^2/(ab+bc-a^2+ab+bc-b^2+ac+bc-c^2)`
`A>=(a^2+b^2+c^2+2ab+2bc+2ca)/(2ab+2bc+2ca-a^2-b^2-c^2)`
`text{CMBĐT phụ}`
`x^2+y^2+z^2>=xy+yz+zx`
`<=>2x^2+2y^2+2z^2>=2xy+2yz+2zx`
`<=>(x^2-2xy+y^2)+(y^2-2yz+z^2)+(z^2-2zx+x^2)>=0`
`<=>(x-y)^2+(y-z)^2+(z-x)^2>=0` `text{luôn đúng}`
`text{Dấu = xảy ra khi x=y=z}`
`text{Áp dụng bài toán phụ trên}`
`2ab+2bc+2ca<=2a^2+2b^2+2c^2`
`<=>2ab+2bc+2c-a^2-b^2-c^2<=a^2+b^2+c^2`
`+)a^2+b^2+c^2>=ab+bc+ca`
`<=>3(a^2+b^2+c^2)<=(a+b+c)^2`
`=>A>=[3(a^2+b^2+c^2)]/(a^2+b^2+c^2)=3(ĐPCM)`
`text{Dấu = xảy ra khi a=b=c}`
