令a^x = b^y = c^z = k
两边取lg得
xlga = ylgb = zlgc = lgk
x = lgk/lga, y = lgk/lgb, z = lgk / lgc
1/x, 1/y, 1/z成等差数列,则2/y = 1/x + 1/z
即2lgb/lgk = lga/lgk + lgc/lgk
2lgb = lga + lgc
b^2 = ac
只能解到这一步了,要求出a,b,c的值,需要其他条件.
已知a.b.c.x.y.z都是不等1的函数,且a^x=b^y=c^z,1/x,1/y,1/z,成等差数列,求a.b.c
3个回答
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