已知x+y=4,xy=-12 求(y+1/x+1)+(x+1/y+1)的值
1个回答
展开全部
x²+y²=(x+y)²-2xy=(-4)²-2×(-12)=40
(y+1)/(x+1)+(x+1)/(y+1)
通分得
=[(y+1)²+(x+1)²]/[(x+1)(y+1)]
展开得
=[y²+2y+1+x²+2x+1]/(xy+x+y+1)
=[(x²+y²)+2(x+y)+2]/[xy+(x+y)+1]
代入已知量
=(40+2×(-4)+2)/(-12+(-4)+1)
=34/(-15)
=-34/15
(y+1)/(x+1)+(x+1)/(y+1)
通分得
=[(y+1)²+(x+1)²]/[(x+1)(y+1)]
展开得
=[y²+2y+1+x²+2x+1]/(xy+x+y+1)
=[(x²+y²)+2(x+y)+2]/[xy+(x+y)+1]
代入已知量
=(40+2×(-4)+2)/(-12+(-4)+1)
=34/(-15)
=-34/15
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