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ASU 178 All Soviet Union MO 1973 |ax^2+bx+c|\le 1 => |cx^2+bx+a| \le 2

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July 4, 2019
algebratrinomialinequalities

Problem Statement

The real numbers a,b,ca,b,c satisfy the condition:
for all xx, such that for −1≤x≤1 -1 \le x \le 1, the inequality ∣ax2+bx+c∣≤1| ax^2 + bx + c | \le 1 is held. Prove that for the same xx , ∣cx2+bx+a∣≤2| cx^2 + bx + a | \le 2
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