Equal Values Force a Sum

★ 7/10calculus Monotonicity inequality Symmetry

Problem

Let

f(x) = \frac{(x-1)\ln x}{x},

and suppose $f(x_1) = f(x_2)$ with $x_1 \neq x_2$ . Prove that $x_1 + x_2 > 2$ .

Answer

Solution

Difficulty	7/10
Topics	calculus, Monotonicity, inequality, Symmetry

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