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Two Sets

Source: 2003 National High School Mathematics League, Exam One, Problem 9

March 16, 2020

Problem Statement

Two sets A={x∈R∣x2−4x+3<0},B={x∈R∣21−x+a≤0,x2−2(a+7)x+5≤0}A=\{x\in\mathbb{R}|x^2-4x+3<0\},B=\{x\in\mathbb{R}|2^{1-x}+a\leq0,x^2-2(a+7)x+5\leq0\}. If A⊆BA\subseteq B, then the range value of real number aa is________.
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