已知A,B,C的对数是a,b,c,且a+b+c=0,证明:A(1/b+1/c)×B(1/a+1/c)×C(1/a+1/b)=1/1000(1/b+1/c)是A的指数 1/a+1/c)是B的指数 (1/a+1/b)是C的指数学生升到高中去了,回来问了一个问题,学校的老师
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![已知A,B,C的对数是a,b,c,且a+b+c=0,证明:A(1/b+1/c)×B(1/a+1/c)×C(1/a+1/b)=1/1000(1/b+1/c)是A的指数 1/a+1/c)是B的指数 (1/a+1/b)是C的指数学生升到高中去了,回来问了一个问题,学校的老师](/uploads/image/z/7023588-60-8.jpg?t=%E5%B7%B2%E7%9F%A5A%2CB%2CC%E7%9A%84%E5%AF%B9%E6%95%B0%E6%98%AFa%2Cb%2Cc%2C%E4%B8%94a%2Bb%2Bc%3D0%2C%E8%AF%81%E6%98%8E%EF%BC%9AA%EF%BC%881%2Fb%2B1%2Fc%EF%BC%89%C3%97B%EF%BC%881%2Fa%2B1%2Fc%EF%BC%89%C3%97C%EF%BC%881%2Fa%2B1%2Fb%EF%BC%89%3D1%2F1000%EF%BC%881%2Fb%2B1%2Fc%EF%BC%89%E6%98%AFA%E7%9A%84%E6%8C%87%E6%95%B0+1%2Fa%2B1%2Fc%EF%BC%89%E6%98%AFB%E7%9A%84%E6%8C%87%E6%95%B0+%EF%BC%881%2Fa%2B1%2Fb%EF%BC%89%E6%98%AFC%E7%9A%84%E6%8C%87%E6%95%B0%E5%AD%A6%E7%94%9F%E5%8D%87%E5%88%B0%E9%AB%98%E4%B8%AD%E5%8E%BB%E4%BA%86%EF%BC%8C%E5%9B%9E%E6%9D%A5%E9%97%AE%E4%BA%86%E4%B8%80%E4%B8%AA%E9%97%AE%E9%A2%98%EF%BC%8C%E5%AD%A6%E6%A0%A1%E7%9A%84%E8%80%81%E5%B8%88)
已知A,B,C的对数是a,b,c,且a+b+c=0,证明:A(1/b+1/c)×B(1/a+1/c)×C(1/a+1/b)=1/1000(1/b+1/c)是A的指数 1/a+1/c)是B的指数 (1/a+1/b)是C的指数学生升到高中去了,回来问了一个问题,学校的老师
已知A,B,C的对数是a,b,c,且a+b+c=0,证明:A(1/b+1/c)×B(1/a+1/c)×C(1/a+1/b)=1/1000
(1/b+1/c)是A的指数 1/a+1/c)是B的指数 (1/a+1/b)是C的指数
学生升到高中去了,回来问了一个问题,学校的老师都做不出来啊。
已知A,B,C的对数是a,b,c,且a+b+c=0,证明:A(1/b+1/c)×B(1/a+1/c)×C(1/a+1/b)=1/1000(1/b+1/c)是A的指数 1/a+1/c)是B的指数 (1/a+1/b)是C的指数学生升到高中去了,回来问了一个问题,学校的老师
对【A(1/b+1/c)×B(1/a+1/c)×C(1/a+1/b)】取对数,经过一定处理后,代入a+b+c=0
lg【A^(1/b+1/c)×B^(1/a+1/c)×C^(1/a+1/b)】=(1/b+1/c)lgA+(1/a+1/c)lgB+(1/a+1/b)lgC=a/b+a/c+b/a+b/c+c/a+c/b
a+b+c=0 ,c=-a-b,a=-b-c,b=-a-c
a/b+a/c+b/a+b/c+c/a+c/b
=(-b-c)/b+(-b-c)/c+(-a-c)/a
=-1-c/b-b/c-1-1-c/a+b/c+c/a+c/b
=-3
lg【A^(1/b+1/c)×B^(1/a+1/c)×C^(1/a+1/b)】=-3
所以A^(1/b+1/c)×B^(1/a+1/c)×C^(1/a+1/b)=10^(-3)=1/1000