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本文对《数学通报》的以下两个问题进行了简证及统一研究.问题1 2010年11月第1885号数学问题:已知a,b,c为正数,求证:9a/b+c+16b/c+a+25c/a+b≥22.问题2 2013年1月第2103号数学问题:设a,b,c为△ABC的三边长,x,y,z为正数,求证:ax2/b+c-a+bx2/c+a-b+cx2/a+b-c≥xy+yz+zx.
In this paper, we summarize and unify the following two questions in the “Mathematics Bulletin”: Problem 1 Mathematical Problem No. 1885 in November 2010: It is known that a, b and c are positive numbers, and the proof is: 9a / b + c + 16b / c + a + 25c / a + b≥22. Question 2 Mathematics No. 2103 of January 2013: Let a, b, c be the length of the sides of △ ABC, and x, y, z be positive numbers. : ax2 / b + c-a + bx2 / c + a-b + cx2 / a + bc ≧ xy + yz + zx.