已知y+z分之x =a ,x+z分之y =b ,x+y分之z =c,试求a+1分之a + b+1分之b + c+1分之c 的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 11:17:58
已知y+z分之x =a ,x+z分之y =b ,x+y分之z =c,试求a+1分之a + b+1分之b + c+1分之c 的值

已知y+z分之x =a ,x+z分之y =b ,x+y分之z =c,试求a+1分之a + b+1分之b + c+1分之c 的值
已知y+z分之x =a ,x+z分之y =b ,x+y分之z =c,试求a+1分之a + b+1分之b + c+1分之c 的值

已知y+z分之x =a ,x+z分之y =b ,x+y分之z =c,试求a+1分之a + b+1分之b + c+1分之c 的值
因为:
a/(a+1)=[x/(y+z)]/[(x+y+z)/(y+z)]=x/(x+y+z)
b/(b+1)=[y/(x+z)]/[(x+y+z)/(x+z)]=y/(x+y+z)
c/(c+1)=[z/(x+y)]/[(x+y+z)/(x+y)]=z/(x+y+z)
所以
a/(a+1)+b/(b+1)+c/(c+1)=x/(x+y+z)+y/(x+y+z)+z/(x+y+z)=(x+y+z)/(x+y+z)=1

已知实数X.Y.Z满足(Y+Z)分之X+(Z+X)分之Y+(X+Y)分之Z=1,则(Y+Z)分之X平方+(Z+X)分之Y平方+(X+Y)分之Z平方的值为( ) 已知z分之x+y=x分之y+z=y分之x+z=k 若z分之x+y+z=y分之x-y+z=x分之-x+y+z,求xyz分之(x+y)(y+z)(z+x) x分之y+z=y分之z+x=z分之x+y(x+y+z不等于0),求x+y+z分之x+y-z 已知y+z分之x=x+z分之y=x+y分之z 求y+z分之x的值 已知a-b分之x=b-c分之y=c-a分之z(abc互不相等).已知a-b分之x=b-c分之y=c-a分之z(abc互不相等).已知z分之x+y=y分之x+Z=x分之y+Z(xyz≠0,x+y+z≠0),求x+y+z分之x+y-z的值 已知z分之(x+y)=x分之(y+z)=y分之(x+z)=k,(x+y+z≠0).求(x+y+z)分之(x+y-z)的值.要具体过程! 已知y+z分之x=z+x分之y=x+y分之z(x+y+z≠0)求x-y+z分之x+2y+z的值 已知x分之y+z=y分之z+x=z分之x+y,其中x+y+z≠0求·x+y+z分之x+y-z的值 已知x分之y+z=y分之z+x=z分之x+y,其中x+y+z≠0求·x+y+z分之x+y-z的值 已知5分之X+Y=6分之Y+Z=7分之x+z,且X,Y,Z都不等于0,求X:Y:Z的值 (x-2y+z)(x+y-2z)分之(y-x)(z-x) + (x+y-2z)(y+z-2x)分之(z-y)(x-y) + (y+z-2z)(x-2y+z)分之(x-z)(y-z)=?第三部分那个是 (y+z-2x)(x-2y+z)分之(x-z)(y-z) 已知有理数X、Y、Z互不相等,则Y-Z分之X-Y、Z-X分之Y-Z、X-Y分之Z-X,中负数有几个? z分之x+y=x分之y+z=y分之z+x,则xyz分之(x+y)(y+z)(Z+x)=? 已知x+y+z=0,求x(y分之1+z分之)+y(x分之一+z分之一)+z(x分之一+y分之一)的值 已知X分之Y+Z-X=y分之X+Z-Y=Z分之X+Y-Z,求XZ分之(X+Y)(Y+Z)的值 已知x+y+z=3x=2y,求x+y+z分之z的值 已知y+z分之x =a ,x+z分之y =b ,x+y分之z =c,试求a+1分之a + b+1分之b + c+1分之c 的值