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若 $f(u, v)$ 的二阶偏导数连续，且满足：$\frac{\partial^2 f}{\partial u^2}+\frac{\partial^2 f}{\partial v^2}=1$ ．又 $z=f\left(x y, \frac{x^2-y^2}{2}\right)$ ， $\frac{\partial^2 z}{\partial x^2}+\frac{\partial^2 z}{\partial y^2}=$
                        
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