Question

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

Answer 1

$(sqrt3)^{log_3(sqrt5-2)^2}=3^{log_3(sqrt5-2)}=sqrt5-2\sqrt2^{log_2(sqrt5-3)^2}=2^{log_2(3-sqrt5)}=3-sqrt5\\sqrt5-2+3-sqrt5=1$