Question

已知x+y=-4,xy=-12,求y+1/x+1+x+1/y+1 的值

已知x+y=-4,xy=-12,求y+1/x+1+x+1/y+1 的值

Answer 1

y+1/x+1+x+1/y+1
=(y+1)²+（x+1)²/(x+1)(y+1)
=y²+2y+1+x²+2x+1/xy+x+y+1
=(x+y)²+2(x+y)+2-2xy/xy+x+y+1
把x+y=-4 xy=-12 代入上式
解得：y+1/x+1+x+1/y+1= ﹣34/15
采纳吧 亲 这么晚写滴 挺辛苦哦

Answer 2

原式=(y＋1)/(x＋1)＋(x＋1)/(y＋1)
=[(y＋1)²＋(x＋1)²]/[(x＋1)(y＋1)]
=[x²＋y²＋2x＋2y＋2]/[x＋y＋xy＋1]
=[(x＋y)²－2xy＋2(x＋y)＋2]/[(x＋y)＋(xy)＋1]
=[16－24＋8＋2]/[－4－12＋1]
=－2/15

Answer 3

y+1/x+1+x+1/y+1
=[(y+1)²+(x+1)²]/[(x+1)(y+1)]
=[x²+y²+2(x+y)+2]/(x+y+xy+1)
=[(x+y)²+2(x+y)-2xy+2]/(x+y+xy+1)
=[(-4)²+2x(-4)-2x(-12)+2]/(-4-12+1)=-34/15