Răspuns:
[tex] log_{2}( \sqrt{2 + \sqrt{2} } ) + log_{2}( \sqrt{2 - \sqrt{2} } ) = log_{2}( \sqrt{2 + \sqrt{2} } \times \sqrt{2 - \sqrt{2} } ) = log_{2}( \sqrt{(2 + \sqrt{2})(2 - \sqrt{2} } ) = log_{2}( \sqrt{4 - 2} ) = log_{2}( \sqrt{2} ) = log_{2}( {2}^{ \frac{1}{2} } ) = \frac{1}{2} log_{2}(2) = \frac{1}{2} [/tex]
