已知:x+ 1/(y+1)=5, y+ 1/(z+1)=2,z+ 1/(x+1)=10/3, 求:(x+1)(y+1)(z+1)急!在线候着,请教数学好的大虾们!

已知:x+ 1/(y+1)=5, y+ 1/(z+1)=2,z+ 1/(x+1)=10/3, 求:(x+1)(y+1)(z+1)急!在线候着,请教数学好的大虾们!
已知:x+ 1/(y+1)=5, y+ 1/(z+1)=2,z+ 1/(x+1)=10/3, 求:(x+1)(y+1)(z+1)
急!在线候着,请教数学好的大虾们!

已知:x+ 1/(y+1)=5, y+ 1/(z+1)=2,z+ 1/(x+1)=10/3, 求:(x+1)(y+1)(z+1)急!在线候着,请教数学好的大虾们!
首先换元设X+1=A,Y+1=B,Z+1=C,则方程变为
A+1/B=6,B+1/C=3.C+1/A=13/3,求A*B*C的值
根据上式有AB+1=6B,BC+1=3C,CA+1=13/3A
将上式连乘从而有
（AB+1)(BC+1)(CA+1)/ABC=78
将上式展开,得
ABC+A+B+C+1/A+1/B+1/C+1/ABC=78
根据前面所给条件
得ABC+1/ABC=78-6-3-13/3=194/3
解出答案为97/3+2/3*2491^(1/2)或97/3-2/3*2491^(1/2 )