求证:无论x、y为何值,4x2-12x+9y2+30y+35的值恒为正.

问题描述:

求证:无论x、y为何值,4x2-12x+9y2+30y+35的值恒为正.

∵4x2-12x+9y2+30y+35=4x2-12x+9+9y2+30y+25-9-25+35=(2x-3)2+(3y+5)2+1≥1,
∴多项式4x2-12x+9y2+30y+35的值恒为正.