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Antonache Emanuel
Euclid
Posts: 37
Joined: Sat Feb 28, 2009 4:15 pm
Location: Targoviste, Dambovita

Shortlist 15

Post by Antonache Emanuel »

Sa se arate ca ecuatia \( 5^x+6^{\frac{1}{x}}+7^{x+\frac{1}{x}}=58 \) nu admite solutii in multimea numerelor reale.
Mariana Coada, Shortlist 2004
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Marius Mainea
Gauss
Posts: 1077
Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Post by Marius Mainea »

\( LHS\ge 5^x+5^{\frac{1}{x}}+7^{x+\frac{1}{x}}\ge 2\cdot 5^{\frac{x+\frac{1}{x}}{2}}+7^2\ge10+49=59>RHS \)
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