求证,无论xy取何值,4x^2-12x+9y^2+30y+35的值恒为正

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/05 02:50:27
求证,无论xy取何值,4x^2-12x+9y^2+30y+35的值恒为正

求证,无论xy取何值,4x^2-12x+9y^2+30y+35的值恒为正
求证,无论xy取何值,4x^2-12x+9y^2+30y+35的值恒为正

求证,无论xy取何值,4x^2-12x+9y^2+30y+35的值恒为正
4x^2-12x+9y^2+30y+35=(2x-3)^2+(3x+5)^2+1>=1
所以恒为正数

4x^2-12x+9y^2+30y+35
=4(x-3/2)^2-9+9(y+5/3)^2-25+35
=4(x-3/2)^2+9(y+5/3)^2+1
>=1
xy取何值,4x^2-12x+9y^2+30y+35的值恒为正