Объяснение:

[tex]\displaystyle\\(\sqrt{5})^{2log_5(\sqrt{2}-1)} +(\sqrt{3})^{log_3(\sqrt{2}-2)} =(\sqrt{5})^{log_5(\sqrt{2}-1)^2} +(\sqrt{3})^{2log_3(\sqrt{2}-2)} = \\\\=((\sqrt{5})^2)^{log_5(\sqrt{2}-1)} +((\sqrt{3})^2)^{log_3(\sqrt{2}-2)} =5^{log_5(\sqrt{2}-1)} +3^{log_3(\sqrt{2}-2)} =\\\\=|\sqrt{2}-1|+|\sqrt{2}-2|=\sqrt{2}-1+2-\sqrt{2}=1.[/tex]