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例1设x,y为实数,且x~2+xy+y~2= 3,求x~2-xy+y~2的最大值和最小值。分析已知条件和待求式都是二次齐次式,可采用判别式法求x~2-xy+y~2的最值。
Example 1 Let x and y be real numbers and x~2+xy+y~2=3. Find the maximum and minimum values of x~2-xy+y~2. The analysis of the known conditions and the pending formulas are all of the second-order homogeneous method. The discriminant method can be used to find the best value of x~2-xy+y~2.