已知27^2=a^6=81^b,求(a-1/5b)^2-(a+1/5)(a-1/5b)+2b(a-1/25b)的值
问题描述:
已知27^2=a^6=81^b,求(a-1/5b)^2-(a+1/5)(a-1/5b)+2b(a-1/25b)的值
答
27^2=a^6=81^b3^6=a^6=3^4ba=3b=3/2(a-1/5b)^2-(a+1/5b)(a-1/5b)+2b(a-1/25b)=(a-1/5b)(a-1/5b-a-1/5b)+2b(a-1/25b)=2b(a-1/25b)-2b/5(a-1/5b)=2b(a-1/25b-1/5a+1/25b)=2b*(4a/5)=8ab/5=8/5×3×3/2=36/5