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构造方程解题,方法巧妙,过程简明,对此已有许多杂志载文介绍。然而,我们发现常常发生下面的错误。现抄录两例加以分析,以期引起大家注意。 例1 若a、b为实数,且a~2+3a+1=0,b~2+3b+1=0,求b/a+a/b的值。 解:由已知及方程的定义可知,a、b是方程x~2+3x+1=0的两根,由韦达定理得a+b=-3,ab=1。
Construct equations to solve problems, clever methods, and concise processes, which have been published in many magazines. However, we have found that the following errors occur frequently. Two cases are transcribed and analyzed to draw attention. Example 1 If a and b are real numbers and a~2+3a+1=0 and b~2+3b+1=0, find the value of b/a+a/b. Solution: From the definition of the known and equations, a and b are the two equations x~2+3x+1=0. Weedta’s theorem yields a+b=-3, ab=1.