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本文与同学们谈一谈不等式(组)在数学竞赛中的4种常规应用,以开阔同学们的解题视野,提高同学们的解题能力,下面举例加以说明,供同学们学习时参考.一、用于求值例1已知函数x,y,z满足3x+2y-z=4,2x-y+2z=6.x+y+z<7求x+y+z的值解:将已知等式相加得5x+y+z=10,∴10-4x=x+y+z<7,∴x>3/4,∵y,z为正整数,∴5x=10-y-z≤
This article talks with students about the four kinds of general applications of inequality (group) in mathematics competition so as to broaden their students ’problem-solving perspective and improve the students’ ability to solve problems. The following examples give the students reference when learning. First, for evaluation Example 1 Known functions x, y, z satisfy 3x + 2y-z = 4,2x-y + 2z = 6.x + y + z <7 Find the value of x + y + z Solution: Add known equations 5x + y + z = 10, ∴10-4x = x + y + z <7, ∴x> 3/4, ∵y, z is a positive integer, ∴5x = 10-yz ≤