You have to have a condition : \(a,b>0\)

a) \(\left(a+b\right)^2\ge4ab\)

<=> \(a^2+2ab+b^2\ge4ab\)

<=>  \(a^2-2ab+b^2\ge0\)

<=>  \(\left(a-b\right)^2\ge0\)  (It's true)

=> \(\left(a+b\right)^2\ge4ab\)

b) Applying Cauchy's inequality , we have

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

Equation occur <=> a = b 

You have to have a condition : a,b>0

a) (a+b)2≥4ab

<=> a2+2ab+b2≥4ab

<=>  a2−2ab+b2≥0

<=>  (a−b)2≥0

  (It's true)

=> (a+b)2≥4ab

b) Applying Cauchy's inequality , we have

a+b≥2ab−−√

Equation occur <=> a = b