不等式是高中阶段的重要知识点之一,不等式的最值问题的解法为高中生思维方式的拓展提供一条训练捷径.本文介绍一道易错题的多条解题路径,供同学们参考.题目设a,b,x,y∈R,且满足a2+b2=p2,x2+y2=q2(p>0,q>0,p≠q),求ax+by的最大值.常见错误因为a2+b2=p2,x2+y2=q2(p>0,q>0),所以 Inequality is one of the important knowledge points in senior high school, and the solution of the most significant problem of inequality provides a training shortcut for the development of senior high school students’ thinking mode.This paper introduces a number of easy ways to solve problems, for students to reference. a, b, x, y∈R, and satisfy a2 + b2 = p2, x2 + y2 = q2 (p> 0, q> 0, p ≠ q) b2 = p2, x2 + y2 = q2 (p> 0, q> 0), so