若|3a+4b-c|+14(c-2b)2=0,则a:b:c=______.-数学

题目简介

若|3a+4b-c|+14(c-2b)2=0,则a:b:c=______.-数学

题目详情

若|3a+4b-c|+
1
4
(c-2b)2=0,则a:b:c=______.
题型:填空题难度:中档来源:不详

答案

依题意得:|3a+4b-c|=0,且(c-2b)2=0,
c=2b①
3a+4b-2b=0②

∴由②得3a=-2b,即a=-class="stub"2
3
b,
∴a:b:c=-class="stub"2
3
b:b:2b=-2:3:6.
故答案为:-2:3:6.

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