1.若实数X Y Z满足X+1/Y=4,Y+1/Z=1,Z+1/X=7/3,求XYZ乘积~

题目

1.若实数X Y Z满足X+1/Y=4,Y+1/Z=1,Z+1/X=7/3,求XYZ乘积~
2.已知2X-3/(X-1)(X+2)=A/X-1+B/X+2,求A,B值
3.已知2X+5Y,求X-Y/X+Y
4.甲乙合打一份稿件,甲每分钟打M个字,乙每分钟打30个字,已知这份稿件共25000个字,甲乙两人各打一半,那么打完这份稿件共用了多少时间?
3.应该是2X=5Y,求X-Y/X+Y

答案

(x+1/y)(y+1/z)(z+1/x)=28/3
将其展开为
xyz+x+y+z+1/x+1/y+1/z+1/xyz=28/3①
将已知的三个因式相加得到
xyz+x+y+z+1/x+1/y+1/z=22/3②
①-②=2
即xyz+1/xyz=2
假设xyz=a
则a+1/a=2
得 a2-2a+1=0(a2表示a的平方)
得 a=1
即 x*y*z=1
A/x-1+B/x+2=(Ax+2A+Bx-B)/(x-1)(x+2)
=[(A+B)x+2A-B]/(X-1)(X+2)
(2X-3)/(X-1)(X+2)=[(A+B)X+2A-B]/(X-1)(X+2)
{A+B=2
{2A-B=-3
所以A=-1/3 B=7/3