若实数a,b满足log2(a-2)+log2(2b-2)=3,则a+b的最小值为?
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若实数a,b满足log2(a-2)+log2(2b-2)=3,则a+b的最小值为?若实数a,b满足log2(a-2)+log2(2b-2)=3,则a+b的最小值为?若实数a,b满足log2(a-2)+
若实数a,b满足log2(a-2)+log2(2b-2)=3,则a+b的最小值为?
若实数a,b满足log2(a-2)+log2(2b-2)=3,则a+b的最小值为?
若实数a,b满足log2(a-2)+log2(2b-2)=3,则a+b的最小值为?
由已知得 (a-2)(2b-2) = 8 ,
所以 (2a-4)(2b-2) = 16 ,
根据均值定理得 (2a-4)+(2b-2) ≥ 2√[(2a-4)(2b-2)] = 8 ,
所以可得 a+b ≥ 7 ,
当且仅当 2a-4 = 2b-2 且 (a-2)(2b-2) = 8 ,也即 a = 4,b = 3 时,a+b 最小值为 7 .
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