A Log-Ratio Bound

★ 8/10calculus Substitution Estimation inequality Vieta's Formulas

Problem

The function $f(x) = \mathrm{e}^x - ax$ has two zeros $x_1, x_2$ . Prove that

\left|\ln\frac{x_1}{x_2}\right| < \sqrt{a^2 - 2a - 1}\cdot x_1 x_2.

Answer

Solution

Difficulty	8/10
Topics	calculus, Substitution, Estimation, inequality, Vieta's Formulas

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