MathDB

3

Part of 1986 National High School Mathematics League

Problems(2)

Inequality?

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

2/24/2020
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]
inequalities
Integral Points

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

2/24/2020
In rectangular coordinate system, define that if and only if both xx-axis and yy-axis of a point are integers, we call it integral point. Please color all intengral points in white, red and black, satisfying: (1) Points in every color appear on infinitely many lines that are parallel to xx-axis. (2) For any white point AA, red point BB, black point CC, we can find another red point DD, such that ABCDABCD is a parallelogram.
calculusintegration