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有些练习题所要求解决的问题,表面上看并非属于某类方程。但是,如果在解题过程中,适当地制作辅助方程,可能使问题解决得更为方便一些。例如在实数范围内将二次多项式3x~2-5x-11分解为两个一次因式的乘积。我们引进一个辅助方程3x~2-5x-10=0,应用公式解得 X=5±(157~(1/2)),于是得到 3x~2-5x-11=3(x-(5+157~(1/2))/6 x-(5-(157~(1/2))/6 又如,解方程组x+y=a,xy=b.时,可制作一种方程u~2-au+b=0,求得u_1、u_2,从而方便地得到方程组的二解为x=u_1,y=u_2;及x=u_2,y=u_1。再如求函数y=ax~2+bx+c的极值时,我们
Some of the problems that are required to be solved by the exercises are, on the surface, not certain types of equations. However, if the auxiliary equations are properly made during the problem solving process, the problem may be solved more easily. For example, the quadratic polynomial 3x~2-5x-11 is decomposed into a product of two primary factors in the real range. We introduce an auxiliary equation 3x~2-5x-10=0, and use the formula to solve X=5±(157~(1/2)), so we get 3x~2-5x-11=3(x-(5+) 157~(1/2))/6 x-(5-(157~(1/2))/6 Another example, solving equations x+y=a, xy=b. If ~2-au+b=0, find u_1, u_2, so that the two solutions of the system of equations are conveniently x=u_1,y=u_2, and x=u_2,y=u_1. Again, find the function y=ax~ When the extreme value of 2+bx+c, we