解方程[(19x-x^2)/(x+1)][x+(19-x)/(x+1)]=84.

题目

解方程[(19x-x^2)/(x+1)][x+(19-x)/(x+1)]=84.

答案

记y=(19-x)/(x+1),1)a=x+y则方程化为：xy [x+y]=84,2)由1),得：xy+y=19-x,即xy=19-x-y=19-a代入2）得：(19-a)a=84a^2-19a+84=0(a-7)(a-12)=0a=7,12故xy=19-a=12,7解x+y=7,xy=12,得：x,y=3,4解x+y=12,xy=7,得：x,y=6+...