2008 IMO 第 4 题

Find all functions $f$ from the positive reals to the positive reals such that

$$\frac{f(w)^{2} + f(x)^{2}}{f(y^{2}) + f(z^{2})} = \frac{w^{2} + x^{2}}{y^{2} + z^{2}}$$

for all positive real numbers $w$ , $x$ , $y$ , $z$ satisfying $wx = yz$ .

找到从正实数到正实数的所有函数 $f$ ，使得

$$\frac{f(w)^{2} + f(x)^{2}}{f(y^{2}) + f(z^{2})} = \frac{w^{2} + x^{2}}{y^{2} + z^{2}}$$

对于所有正实数 $w$ 、 $x$ 、 $y$ 、 $z$ 满足 $wx = yz$ 。