若x^2-x=4,y^2-y=4,且x不等于y.则x^2+2xy+y^2=?

题目

若x^2-x=4,y^2-y=4,且x不等于y.则x^2+2xy+y^2=?

答案

x^2-x=4,y^2-y=4则x,y都是方程 A²-A-4=0的根.利用韦达定理x+y=1∴ x^2+2xy+y^2=(x+y)²=1如果没有学过韦达定理x^2-x=4, ①y^2-y=4 ②①-②x²-y²-(x-y)=0∴(x-y)(x+y)=x-y∵ x≠y∴ x-y≠0∴ x+...