论文部分内容阅读
设P(x,y)=ax~2+bxy+cy~2+dx+ey+f,在什么条件下P(x,y)可分解成两个一次因式的积,对于解二元二次不定方程是十分重要的,本文给出P(x,y)可分解成两个一次因式乘积的充要条件,并举例说明如何具体应用,cy~2+dx+ey+f(a≠0)可分解成两个一次证明将P(x,y)按x降幂排列 P(x,y)=ax~2+(by+d)x+(cy~2+ey+f) (1) 视y为参数,P(x,y)能分解成两个一次因式乘积的充要条件是关于x的二次三项式(1)的判
Let P(x,y)=ax~2+bxy+cy~2+dx+ey+f, under what conditions P(x,y) can be decomposed into the product of two one-factors for the solution binary two. The indefinite equation is very important. In this paper, the necessary and sufficient conditions for P(x,y) to be decomposed into two one-factor products are given, and an example is given to show how to apply it. cy~2+dx+ey+f(a≠ 0) Decomposes into two proofs P(x,y) is decomposed by x P(x,y)=ax~2+(by+d)x+(cy~2+ey+f) (1) Considering y as a parameter, the necessary and sufficient condition for P(x,y) to be decomposed into two products of one factorial is the judgment of quadratic trinomial (1) on x.