千变万化的数学问题中常常隐含着某个“不变量”,而这个不变量往往是解决问题的突破口.如几何问题中的面积就是常见的“不变量”,灵活巧妙地利用这一不变量求解几何问题的方法称之为“面积法”.下面举例说明.一、证明代数问题例1已知:x、y、z、r均为正数,且x2+y2=z2,z x2-r2=x2 The ever-changing mathematical problem often implies an “invariant”, and this invariant is often the breakthrough point for solving the problem. If the area in the geometric problem is a common “invariant”, the invariant solution can be flexibly and flexibly utilized. The method of geometry problem is called “area method”. Here is an example to illustrate. First, proof algebra problem Example 1 is known: x, y, z, r are all positive, and x2 + y2 = z2, z x2-r2 = X2