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$$\sqrt{x+a_1}+\sqrt{x+a_2}+\ldots+\sqrt{x+a_n}=n\sqrt{x}$$

Source: Moldova TST 1999

August 7, 2023
equation

Problem Statement

Let a1,a2,…,ana_1, a_2, \ldots, a_n be real numbers, but not all of them null. Show that the equation x+a1+x+a2+…+x+an=nx\sqrt{x+a_1}+\sqrt{x+a_2}+\ldots+\sqrt{x+a_n}=n\sqrt{x} has at most one real solution.
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