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Inequality?

Source: 1986 National High School Mathematics League, Exam One, Problem 3

February 24, 2020
inequalities

Problem Statement

For real numbers a,b,ca,b,c, if a2−bc−8a+7=b2+c2+bc−6a−6=0,a^2-bc-8a+7=b^2+c^2+bc-6a-6=0, then the range value of aa is (A)(−∞,+∞)(B)(−∞,1]∪[9,+∞)(C)(0,7)(D)[1,9]\text{(A)}(-\infty,+\infty)\qquad\text{(B)}(-\infty,1]\cup[9,+\infty)\qquad\text{(C)}(0,7)\qquad\text{(D)}[1,9]
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