已知a,b,c是非零实数,且a+b+c=2,1/a+1/b+1/c,证明a,b,c中至少有一个等于2
人气：121 ℃ 时间：2019-10-18 16:56:11
解答
1/a+1/b+1/c=1/2两边同乘以2abc得2ab+2bc+2ca=abc又因为a+b+c=2所以(a-2)(b-2)(c-2)=abc-2ab-2bc-2ca+4a+4b+4c-8=2ab+2bc+2ca-2ab-2bc-2ca+4a+4b+4c-8=4a+4b+4c-8=4（a+b+c）-8=4×2- 8=0所以a-2=0或b-2=0或c-2=0即a...
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