1.计算1^/(1^-100+5000)+3^/(3^-300+5000)+5^/(5^-500+5000)+…+99^/(99^-9900+5000)2.若x+y+z=xyz不等于0,计算(1-y^)(1-z^)/yz+(1-x^)(1-z^)/xz+(1-x^)(1-y^)/xy的值3.若x/(y-z)+y/(z-x）+z/(x-y)=0,求证x/(y-z)^+y/(z-x)^+z/(x-y)^=0^为平方

Question

1.计算
1^/(1^-100+5000)+3^/(3^-300+5000)+5^/(5^-500+5000)+…+99^/(99^-9900+5000)
2.若x+y+z=xyz不等于0,计算(1-y^)(1-z^)/yz+(1-x^)(1-z^)/xz+(1-x^)(1-y^)/xy的值
3.若x/(y-z)+y/(z-x）+z/(x-y)=0,求证x/(y-z)^+y/(z-x)^+z/(x-y)^=0
^为平方

Answer 1

1.n^2/(n^2-100n+5000) + (100-n)^2/[(100-n)^2-100(100-n)+5000]
过程就是同分
=2
（这道题的技巧!）
就是说首末两两相加是2
（比如1和99 等等） 除去50（50的话就是50^2/50^2+5000-5000=50^/50^=1）
那么原式=49×2+1=99
2.同分得
原式=x(1-y^)(1-z^)+y(1-x^)(1-z^)+z(1-x^)(1-y^) /xyz
=4
3.x/(y-z)=-y/(z-x)-z/(x-y)==>
x/(y-z)^2=-y/(z-x)(y-z)-z/(x-y)(y-z)=
=[-y(x-y)-z(z-x)]/(x-y)(y-z)(z-x)=
=(y+z-x)/(x-y)(z-x).
==>
y/(z-x)^2=-z/(x-y)(z-x)-x/(y-z)(z-x)
z/(x-y)^2=-x/(y-z)(x-y)-y/(z-x)(x-y)
==>
x/(y-z)^2+y/(z-x)^2+z/(x-y)^2=
=(y+z-x)/(x-y)(z-x)-
-z/(x-y)(z-x)-x/(y-z)(z-x)-
-x/(y-z)(x-y)-y/(z-x)(x-y)=
=-x/(x-y)(z-x)-x/(y-z)(z-x)-x/(y-z)(x-y)=
=-x/(z-x)[1/(x-y)+1/(y-z)]-x/(y-z)(x-y)=
=x/(y-z)(x-y)-x/(y-z)(x-y)=0