近几年双变量问题在模拟题和高考题中越演越烈,成了学生的一块心病。本文结合模拟题和高考题,探讨这类问题的求解思想和工具。一、利用判别式判别式的符号决定一元二次方程根的情况。将函数问题转化成含双变量的方程有解,体现了函数与方程的思想。问题1(2010浙江高考理16)已知平面向量α,β(α≠0,α≠β)满足|β|=1,且α与β-α In recent years, the bivariate problem has become more and more fierce in the simulation and college entrance examination questions, becoming a piece of student’s heart disease. This article combines the simulation and college entrance examination questions to explore such ideas and tools. First, the use of discriminant discriminant symbols determine the root quadratic equation situation. Transforming the function problem into a bivariate equation has the solution, reflecting the idea of ​​function and equation. Problem 1 (2010 Zhejiang college entrance examination reason 16) known plane vector α, β (α ≠ 0, α ≠ β) | β | = 1, and α and β-α