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下面的问题,提供中学生思考练习,解答不必寄来,本期问题解答将在下期发表。欢迎提供适合中学生练习的问题及解答。 1.试证任何整数都可以用三个2来表示。 2.从1,2,3,……,1981这些数中选取一些数,要使其中任何两数的和不能被其差整除,这些数最多可取多少个? 3.设M为弦AB的中点,过M任作两弦CD、EF,联CF、ED与AB相交于K、L,试证:KM=ML。 4.试由下列三式消去x、y,z得a、b、c的关系式。 5.已知双曲线x~2/24tgα-y~2/16ctgα=1(α为锐角)和圆(x-n)~2+y~2=r~2相切于点A((4(3~(1/2)),4)。求α、n、r的值。
The following questions provide middle school students with thinking exercises. Answers do not have to be sent. The questions and answers in this issue will be published in the next issue. Welcome to provide questions and answers for middle school students to practice. 1. Test that any integer can be represented by three twos. 2. Select numbers from the numbers 1,2,3,...,1981, in order to make sure that the sum of any two numbers cannot be divisible by their difference, how many can these numbers be taken? 3. Let M be the middle of the string AB. Point, over M for two strings CD, EF, joint CF, ED and AB intersect in K, L, test: KM = ML. 4. Try to eliminate x, y, z from the following three equations to get the relationship between a, b, and c. 5. Known hyperbola x~2/24tgα-y~2/16ctgα=1 (α is an acute angle) and circle (xn)~2+y~2=r~2 are tangent to point A ((4(3~ (1/2)), 4) Find the values of α, n, and r.