已知27^2=a^6=9^b,求:(a-1/5b)^2+(a+1/5b)^2+2b(a-1/25b)

题目

已知27^2=a^6=9^b,求:(a-1/5b)^2+(a+1/5b)^2+2b(a-1/25b)
已知27^2=a^6=9^b,求:(a-1/5b)^2+(a+1/5b)^2+2b(a-1/25b)的值
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答案

27^2=(3^3)^2=3^6=a^6
所以a=3
9^b=(3^2)^b=3^2b=27^2=3^6
所以2b=6
b=3
(a-1/5b)^2+(a+1/5b)^2+2b(a-1/25b)的值
=a^2-2/5ab+b^2/25+a^2+2/5ab+b^2/25+2ab-2/25b^2
=2a^2+2ab
=2a(a+b)
=2*3*[3+3]
=36