AT-OEMO-FED1 1989 Problem 3

Let $a$ be a real number. Prove that if the equation $x^2-ax+a=0$ has two real roots $x_1$ and $x_2$ , then: $x_1^2+x_2^2 \ge 2(x_1+x_2).$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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