已知x+y=-4,xy=-12，求（y+1/x+1）+（x+1/y+1）的值
2个回答
展开全部
解：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
本回答由提问者推荐
已赞过
已踩过<
评论
收起
你对这个回答的评价是？
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
