求证3x^2-8xy+9y^2-4x+6y+13>0
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求证3x^2-8xy+9y^2-4x+6y+13>0
求证3x^2-8xy+9y^2-4x+6y+13>0
求证3x^2-8xy+9y^2-4x+6y+13>0
左边=(2x²-8xy+8y²)+(x²-4x+4)+(y²+6y+9)
=2(x-2y)²+(x-2)²+(y+3)²≥0
当x-2y=0,x-2=0,y+3=0取等号
但这三个不能同时成立
所以等号取不到
所以3x²-8xy+9y²-4x+6y+13>0
3x^2-8xy+9y^2-4x+6y+13
=2x²-8xy+8y²+x²-4x+4+y²+6y+9
=2(x-2y)²+(x-2)²+(y+3)²
∵(x-2y)²>=0
(x-2)²>=0
(y+3)²>=0
这三个不能同时为0
∴3x^2-8xy+9y^2-4x+6y+13>0
求证3x^2-8xy+9y^2-4x+6y+13>0
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