五、(15分)设 z=z(x,y) 是由方程 (z+dfrac (1)(x),z-dfrac (1)(y))=0 确定的隐函数,且具有连续的-|||-二阶偏导数。求证: ^2dfrac (partial z)(partial x)-(y)^2dfrac (partial z)(partial y)=1 和 ^3dfrac ({partial )^2z}(partial {x)^2}+xy(x-y)dfrac ({partial )^2z}(partial xpartial y)-(y)^3dfrac ({partial )^2z}(partial {y)^2}+2=0