已知x+y=-4,xy=-12,求(x+1/y+1 )+ ( y+1/x+1)的值要写过程啊

问题描述:

已知x+y=-4,xy=-12,求(x+1/y+1 )+ ( y+1/x+1)的值
要写过程啊

x+y=-4,xy=-12,左边除以左边,右边除以右边,得(x+y)/(xy)=1/x+1/y=(-4)/(-12)=1/3,(x+1/y+1 )+ ( y+1/x+1)=x+y+2+1/x+1/y=-4+2+1/3=-5/3

x+y=-4,则(x+y)²=x²+2xy+y²=(-4)²=16所以x²+y²=16-2xy=16+24=40(x+1/y+1 )+ ( y+1/x+1)=(x+1)²/[(x+1)(y+1)]+(y+1)²/[(x+1)(y+1)]=[(x+1)²+(y+1)²]/[(x+1)(y...