Докажите числовое равенство! (√3)^log3(√5-2)^2+(√2)^log2(√5-3)^2=1

[latex](\sqrt3)^{log_3(\sqrt5-2)^2}=3^{log_3(\sqrt5-2)}=\sqrt5-2\\\sqrt2^{log_2(\sqrt5-3)^2}=2^{log_2(3-\sqrt5)}=3-\sqrt5\\\\\sqrt5-2+3-\sqrt5=1[/latex]