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Shortlist 15
Posted:
Sun Mar 28, 2010 8:31 pm
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
Posted:
Sun Mar 28, 2010 10:43 pm
by
Marius Mainea
\( LHS\ge 5^x+5^{\frac{1}{x}}+7^{x+\frac{1}{x}}\ge 2\cdot 5^{\frac{x+\frac{1}{x}}{2}}+7^2\ge10+49=59>RHS \)