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一、观察数量关系例1 已知某三角形的三边分别为2、3~(1/2)、7~(1/2),求此三角形的最大角; 分析:初看似乎要用余弦定理求解;但若观察到2~2+(3~(1/2))=(7~(1/2))~2,可立即求得最大角为90°。例2 a、b、c是三个连续的自然数,且a~2=17689,c~2=18225,则b~2等于( ) (A)17991 (B)18022 (C)17956 (D)17900
First, the observation of the relationship between the number of cases Example 1 Known a triangle of three sides were 2, 3 ~ (1/2), 7 ~ (1/2), seeking the maximum angle of this triangle; Analysis: At first glance, it seems to use cosine theorem Solve; but if you observe 2~2+(3~(1/2))=(7~(1/2))~2, you can immediately find the maximum angle is 90 degrees. Example 2 a, b, and c are three consecutive natural numbers, and a~2=17689, c~2=18225, then b~2 is equal to () (A)17991 (B)18022 (C)17956 (D)17900