Tham khảo
Vì `a>b>0`
`⇒a=b+k(k>0)`
Nên `\frac{a}{b}+\frac{b}{a}`
`=\frac{b+k}{b}+\frac{b}{b+k}`
`=1+\frac{k}{b}+\frac{b}{b+k}`
`=1+\frac{k(b+k)+b.b}{b(b+k)}`
`=1+\frac{bk+k^2+b^2}{b^2+bk}`
`=1+\frac{(bk+b^2)+k^2}{b^2+bk}`
`=1+1+\frac{k^2}{b^2+bk}`
`=2+\frac{k^2}{b^2+bk}`
Nên `\frac{a}{b}+\frac{b}{a}>2`(Không có dấu"`=`".Vì `k>0)`
`\text{©CBT}`