题目

已知x,y,z互不相等,且xyz不等于0,x2＋yz＝z2,y2＋zx＝x2,求证：z2＋xy＝y2

提问时间：2020-08-02

答案

y2＋zx＝x2 => z=(x^2-y^2)/x代入x2＋yz＝z2=> x^4+xy(x^2-y^2)=(x^2-y^2)^2=> x^4+x^3y-xy^3=x^4+y^4-2x^2y^2=> x^3-xy^2-y^3+2x^2y=0z2^＋xy-y^2=x^2＋yz＋xy-y^2=x^2＋y(x^2-y^2)/x＋xy-y^2=x^2-y^3/x＋2xy-y^2=(...