Question

Доказать числовое неравенство.

Answer 1

$( \sqrt{3} )^{log_3( \sqrt{5}-2 )^2}+( \sqrt{2} )^{log_2( \sqrt{5}-3 )^2}= \\\ =( \sqrt{3} )^{log_{ \sqrt{3} } |\sqrt{5}-2 |}+( \sqrt{2} )^{log_{\sqrt{2}}| \sqrt{5}-3|}= \\\ = |\sqrt{5}-2 |+| \sqrt{5}-3|=\sqrt{5}-2 +3- \sqrt{5}=1$