3(a²+2b²)与8ab

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3(a²+2b²)与8ab

3(a²+2b²)与8ab
3(a²+2b²)与8ab

3(a²+2b²)与8ab
3(a²+2b²)-8ab
=3a²-8ab+6b²
=3(a²-8/3ab+2b²)
=3(a²-8/3ab+16/9b²+2/9b²)
=3(a-4/3b)^2+2/3b²
>=0
所以3(a²+2b²)>=8ab

3(a^2+2b^2)>=3*2√[(a^2)*(2b^2)]>=√72丨ab丨>=√64丨ab丨>=8ab
所以3(a^2+2b^2)>=8ab (ab同为0时,取等号)