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A题组新编1.(侯雪花)若a,b是正数,且a+b=1.(1)求证:(a+1/a-1)(b+1/b-1)≥9/4;(2)求证:(a+1/a-1)~2+(b+1/b-1)~2≥9/2;(3)求证:(a+1/a-2)(b+1/b-2)≤1/4;(4)求证:(a+1/a-2)~2+(b+1/b-2)~2≤1/2;
A new group of questions 1. (Hou snow) If a, b is a positive number, and a + b = 1. (1) verification: (a + 1 / a-1) (b + 1 / b-1) ≥ 9 /4; (2) Proof: (a+1/a-1)~2+(b+1/b-1)~2≥9/2; (3) Proof: (a+1/a-2) (b+1/b-2)≤1/4; (4) Proof: (a+1/a-2)~2+(b+1/b-2)~2≤1/2;