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高二数学课外兴趣活动中,老师给我们出了解方程的3个问题: (1) (x~2+2x+3)~(1/2)+(x~3-2x+3)~(1/2) =log_216 (x∈R); (2) (x~2+10x+32)~(1/2)-(x~2-10x+32)~(1/2) =16sin(π/6); (3) ||3x-4|-|3x-8||=2(1993)~0。在活动中,小组同学在解(1)、(2)两题时,都采用移项,两边平方进行求解,解(3)题时,都采用区间讨论法进行求解,他们的做法都求出了结果,我觉得解题步骤冗繁,易出差错,我左思有想,联想到用椭圆、双曲线的定义进行求解,发现了解题的步骤大为简捷,下面给出问题
In the second year of mathematics extracurricular activities of interest, the teacher gave us three questions to understand the equation: (1) (x~2+2x+3)~(1/2)+(x~3-2x+3)~(1/ 2) = log_216 (x∈R); (2) (x~2+10x+32)~(1/2)-(x~2-10x+32)~(1/2)=16sin(π/6) ); (3) ||3x-4|-|3x-8||=2(1993)~0. During the activity, the groupmates used the transfer term when solving the two questions (1) and (2). The squares were solved on both sides. When the (3) question was solved, they were solved by the interval discussion method. Their methods were all found. As a result, I think the problem solving procedure is tedious and error-prone. I think about it and think of using the definition of an ellipse or hyperbole to solve it. I find that the steps for understanding the problem are much simpler. Here are the questions given below.