x²+xy+y²
=x²+xy+y²/4 +3y²/4
=(x+y/2)²+3y²/4
∵(x+y/2)²>=0 3y²/4>=0
∴x²+xy+y²>=0
即x²+xy+y²恒大于0
x²-xy+y² 方法同上
=x²-xy+y²/4 +3y²/4
=(x-y/2)²+3y²/4
∵(x-y/2)²>=0 3y²/4>=0
∴x²-xy+y²>=0
即x²-xy+y²恒大于0
x^2 xy y^2 和 x^2-xy y^2都恒大于零 求证
x²+xy+y²
=x²+xy+y²/4 +3y²/4
=(x+y/2)²+3y²/4
∵(x+y/2)²>=0 3y²/4>=0
∴x²+xy+y²>=0
即x²+xy+y²恒大于0
x²-xy+y² 方法同上
=x²-xy+y²/4 +3y²/4
=(x-y/2)²+3y²/4
∵(x-y/2)²>=0 3y²/4>=0
∴x²-xy+y²>=0
即x²-xy+y²恒大于0