( 1)√((a？ +b？ )/2) ≥ (a+b)/2 ≥√ AB ≥ 2/(1/a+1/b) (the equal sign is true if and only if a=b).

(2)√(ab)≤(a+b)/2 (if and only if a=b, the equal sign holds).

(3) a? +b？ ≥2ab (if and only if a=b, the equal sign holds).

(4)ab≤(a+b)？ /4 (the equal sign holds if and only if a=b).

Basic attribute

1, if x >；; Y, then y < x；; If y

2. If x>y, y & gtz；; So x>z (transitivity).

3. if x>y and z is any real number or algebraic expression, then x+z >; Y+z (addition principle, or additivity of the same inequality).

4. If x>y, z>0, then xz & gtyz；; If x>y, z<0, and then xz.

5. If x>y, m>n, then X+M > Y+n (necessary and sufficient conditions and unnecessary conditions).

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