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极难数学题!高手来~△ABC中三边abc成等比数列,且logc(a)logb(c)loga(b)成等差数列,求证公差d=1.5
极难数学题!高手来~
△ABC中三边abc成等比数列,且logc(a)logb(c)loga(b)成等差数列,求证公差d=1.5
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2020-06-15 22:02
极难数学题!高手来~△ABC中三边abc成等比数列,且logc(a)logb(c)loga(b)成等差数列,求证公差d=1.5
极难数学题!高手来~
△ABC中三边abc成等比数列,且logc(a)logb(c)loga(b)成等差数列,求证公差d=1.5
设b=a*q,c=a*q*q,x=loga(q),对中间一项应用换底公式,logb(c)=loga(c)/loga(b),loga(b)=1+x,loga(c)=1+2x,最后根据三项成等差数列,可列方程:2*(1+2*x)/(1+x)=1/(1+2*x)+1+x解这个三次方程得(其实最后是二次),x=...