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Решите задачу:

$\frac{x+y}{x-y} + \frac{x-y}{x+y}=5 \\ \\ \frac{(x+y)^2+(x-y)^2}{(x-y)(x+y)} =5 \\ \\ \frac{x^2+2xy+y^2+x^2-2xy+y^2}{x^2-y^2} =5 \\ \\ \frac{2x^2+2y^2}{x^2-y^2} =5 \\ \\ \frac{2(x^2+y^2)}{x^2-y^2} =5 \ \ |:2\\ \\ \frac{x^2+y^2}{x^2-y^2} = \frac{5}{2} \\ \\ \frac{x^2+y^2}{x^2-y^2} +\frac{x^2-y^2}{x^2+y^2} = \frac{5}{2}+ \frac{2}{5} =2.5+0.4=2.9 \\ \\ OTBET: \ 2.9$