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

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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
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

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
27^2=a^6=81^b
3^6=a^6=3^4b
a=3
b=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

∵27^2=a^6=81^b
(3³)^2=3^6=a^6=3^4b
∴a=3,b=3/2
原式=a^2-2/5ab+1/25b^2-a^2+1/5ab-1/5a+1/25b+2ab-2/25b^2
=9/5ab-1/5a-1/25b^2
=9/5*3*3/2-1/5*3-1/25*(3/2)^2
= 7.41