已知x+y=-9,xy=20,求y+1/x+1+x+1/y+1 的值

已知x+y=-9,xy=20,求y+1/x+1+x+1/y+1 的值

【参考答案】简便做法：[(y+1)/(x+1)]+[(x+1)/(y+1)]=[(y+1)²+(x+1)²]/[(x+1)(y+1)]=(x²+y²+2x+2y+2)/(xy+x+y+1)=[(x+y)²-2xy+2(x+y)+2]/[xy+(x+y)+1]=[(-9)²-2×20+2×(-9)+2]/[20+(-9)+1]=[81-40-16]/12=25/12======以下答案可供参考======供参考答案1:因为x+y=-9,xy=20所以x²+y²=（x+y）²-2xy=81-40=41，所以（y+1）/（x+1）+（x+1）/（y+1）=（y+1）²/(x+1）(y+1)+（x+1）²/（x+1）（y+1）=[（y+1）²+（x+1）²]/（x+1）（y+1）=(y²+2y+1+x²+2x+1)/(xy+x+y+1)=（41-18+2）/(20-9+1)=25/12供参考答案2:原式=【（y+1)²+(x+1)²]/(x+1)(y+1)=[(x+y)²-2xy+2(x+y)+2]/[xy+(x+y)+1]=(81-40-18+2)/(20-9+1)=25/12供参考答案3:原式=[(x+1)^2+(y+1)^2]/(x+1)(y+1)=[x^2+y^2+2(x+y)+2]/(xy+y+x+1)=[(x+y)^2-2xy+2(x+y)+2]/(xy+x+y+1)把X+Y=-4,XY=-12带入进去得[(-4)^2+24-8+2]/(-15)=-34/15[若原式=(x+1)/(y+1)+(y+1)/(x+1)]x^2为x的平方参考资料：https://zhidao.baidu.com/question/388351602.html

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