Question

Cho : \(a\ge0;b\ge0\)

Chung minh bat dang thuc CAUCHY : \(\frac{a+b}{2}\ge\sqrt{ab}\)

 

Answer 1

\(\left(\sqrt{a}-\sqrt{b}\right)^2\ge0\)

\(a+b-2\sqrt{ab}\ge0\)

\(a+b\ge2\sqrt{ab}\)

\(\frac{a+b}{2}\ge\sqrt{ab}\)

Answer 2

lớp 7 mà chứng minh bất đẳng thức cô-si à @@~

Answer 3

<=>\(\left(a+b\right)^2\ge4ab\)

<=>\(a+b\ge2\sqrt{ab}\)

<=>\(\frac{a+b}{2}\ge\sqrt{ab}\)