已知实数a,b,c,满足a＋b＋c＝1,1/a+b-c+1/b+c-a+1/c+a-b=1,则abc＝_____
<p>问题：已知实数a,b,c,满足a＋b＋c＝1,1/a+b-c+1/b+c-a+1/c+a-b=1,则abc＝_____<p>答案：↓↓↓<p class="nav-title mt10" style="border-top:1px solid #ccc;padding-top: 10px;">郎永强的回答：<div class="content-b">网友采纳 1/(1-2a)+1/(1-2b)+1/(1-2c) =(1-2a-2b+4ab+1-2a-2c+4ac+1-2b-2c+4bc)/(1-2a)(1-2b)(1-2c) =(3-4(a+b+c)+4ab+4ac+4bc)/(1-2a)(1-2b)(1-2c) =(-1+4ab+4ac+4bc)/((1-2a-2b+4ab)(1-2c)) =(-1+4ab+4ac+4bc)/(1-2c-2a+4ac-2b+4bc+4ab-8abc) =1 -1+4ab+4ac+4bc=1-2(a+b+c)+4ac+4bc+4ab-8abc -1=1-2-8abc abc=0
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