Key idea. Move the right side to the left and recognise a square.

1. The difference between the two sides is

   \[a^2+b^2-2ab=(a-b)^2.\]

2. A real number squared is always at least zero. Therefore the left side of the proposed inequality is at least its right side.

3. Equality occurs exactly when \((a-b)^2=0\), which means \(a=b\).

Remember. To prove one expression is at least another, try to write their difference as a square.