For any real number A, B holds, and the equal sign holds if and only if A = B. ..

The process of proof: Since (a-b) 2 ≧ 0, the expanded A 2+b 2-2ab ≧ 0, 2ab is shifted to the right to get the formula A 2+b 2 ≧ 2ab.

Its geometric meaning is that the area of a square is greater than or equal to the sum of the areas of four congruent right triangles in this square.

2. Basic inequality √ab≦(a+b)/2

This inequality requires that both A and B are greater than 0, the equation holds, and the equal sign holds if and only if A = B..

Proof process: To prove (A+B)/2 ≧ AB, you only need to prove A+B ≧ 2 ≧ AB and (A-B) 2 ≧ 0. Obviously, (A-B) 20 is effective.

Its geometric meaning is that the diameter in a circle is twice the product of the two parts of the diameter obtained after being cut by a chord.

3. Basic inequality b/a+a/b≧2

This inequality requires AB > 0, and the equal sign holds if and only if a=b, which means that A and B can be both positive and negative.

The process of proof: B/A+A/B = (A 2+B 2)/AB ≧ 2, just prove A 2+B 2 ≧ 2AB.