已知A=2x^2+4XY-2X-3 B=-X^2+XY+2 且3A+6B的值与X无关，求Y=？
\u5df2\u77e5A=2x\u7684\u5e73\u65b9+4xy-2x-3,B=-x\u7684\u5e73\u65b9+xy+2,\u4e143A+6B\u7684\u503c\u4e0ex\u65e0\u5173\uff0c\u6c42y\u7684\u503c.A=2X^2+4XY-2X-3 B=-X^2+XY+2
\u6240\u4ee53A+6B=3.\uff082X^2+4XY-2X-3\uff09+6.\uff08-X^2+XY+2\uff09
\u6253\u5f00\u62ec\u53f7\u662f6X^2+12\u00b7XY-6X-9-6X^2+6XY+12
\u5408\u5e76\u540c\u7c7b\u9879\u5f97 18XY+3-6X
\u56e0\u5f0f\u5206\u89e3\u5f97 3A+6B= 6X\uff08 3Y-1 \uff09+3
\u56e0\u4e3a3A+6B\u7684\u503c\u4e0eX\u65e0\u5173 \u8bf4\u660e 6X\uff08 3Y-1 ) =0
\u5373 \u5f53Y=1/3\u7684\u65f6\u5019 3Y-1 =0
\u6b64\u65f6\u65e0\u8bba X\u4e3a\u4f55\u503c6X\uff08 3Y-1 \uff09=0 \u56e0\u4e3a0\u4e58\u4ee5\u4efb\u4f55\u6570\u90fd\u7b49\u4e8e0
\u7efc\u4e0a Y=1/3
3A+6B
=3\uff082x^2+4xy-2x-3)+6(-x^2+xy+2)
=6x^2+12xy-6x-9-6x^2+6xy+12
=18xy-6x+3
=x(18y-6)+3
\u591a\u9879\u5f0f\u7684\u503c\u4e0ex\u7684\u53d6\u503c\u65e0\u5173\uff0c\u5219x\u9879\u7cfb\u6570=0
18y-6=0
y=1/3
3A+6B=6x^2+12XY-6X-9+(-6X^2+6XY+12)=18XY-6X+3=6X(3Y-1)+3
3A+6B的值与X无关只能有3Y-1=0即Y=1/3,3A+6B=3与X无关
Y=1/3
3A+6B=18XY-6X+3=(18Y-6)X+3,要使其值与X无关，则必有(18Y-6)=0，所以Y=1/3
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