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八年级 1.(1)如果存在n个整数,其积为n且其和为零,那么数n能被4整除。 (2)如果自然数n能被4整除,试证必存在n个整数它们的乘积为n,而和为零。 2.证明:对任意的非负数a和b,下述不等式成立 1/2(a+b)~2+1/4(a+b)≥ab~(1/2)+ba~(1/2)。 3.平面上有二个等边三角形A_1A_2A_3和B_1B_2B_3,A_1→A_2→A_3与B_1→B_2→B_3为顺时针方向。
Eighth grade 1. (1) If there are n integers whose product is n and its sum is zero, then the number n can be divisible by four. (2) If the natural number n is divisible by four, there must be n integers for the test and their product is n, and the sum is zero. 2. Proof: For any non-negative numbers a and b, the following inequality holds 1/2(a+b)~2+1/4(a+b)≥ab~(1/2)+ba~(1/ 2). 3. There are two equilateral triangles A_1A_2A_3 and B_1B_2B_3 on the plane, and A_1→A_2→A_3 and B_1→B_2→B_3 are clockwise.