Page 1 of 1

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