若(5x+M)^2=25x^2-10xy+N

题目

若(5x+M)^2=25x^2-10xy+N
求M、N

答案

解由(5x+M)^2
=(5x)^2+2×5x×M+M^2
=25x^2-10xM+M^2
又由(5x+M)^2=25x^2-10xy+N
即25x^2-10xM+M^2=25x^2-10xy+N
即M=y
N=M^2
即M=y,N=M^2=y^2.