求证：无论x、y为何值,4x²-12x+9y²+30y+35的值恒为正.

求证：无论x、y为何值,4x²-12x+9y²+30y+35的值恒为正.
求证：无论x、y为何值,4x²-12x+9y²+30y+35的值恒为正.

求证：无论x、y为何值,4x²-12x+9y²+30y+35的值恒为正.
4x^2-12x+9+9y^2+30y+25+1=(2x-3)^2+(3y+5)^2+1
(2x-3)^2≥0,3y+5)^2≥0
(2x-3)^2+(3y+5)^2+1≥1
故恒大于0