Question

Cho a > 2, b > 2. Chứng minh ab > a + b

Answer 1

Ta có:\(a>2,b>2\Rightarrow\dfrac{1}{a}+\dfrac{1}{b}< \dfrac{1}{2}+\dfrac{1}{2}=1\)

\(\Rightarrow\dfrac{b}{ab}+\dfrac{a}{ab}< 1\)

\(\Rightarrow\dfrac{a+b}{ab}< 1\)

\(\Rightarrow a+b< ab\left(đpcm\right)\)

Answer 2

theo đề bài ta có

`\(a>2,b>b\\ \Rightarrow\dfrac{1}{a}+\dfrac{1}{b}< \dfrac{1}{2}+\dfrac{1}{2}=1\\ \Rightarrow\dfrac{1}{a}+\dfrac{1}{b}< 1\\ \Rightarrow\dfrac{b}{ab}+\dfrac{a}{ab}< 1\left(do\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{b}{ab}+\dfrac{a}{ab}\right)\\ \Rightarrow\dfrac{a+b}{ab}< 1\\ \Rightarrow a+b< ab\left(đpcm\right)\)