Tìm min,max

H

huynhbachkhoa23

Đặt $t=x+y+z$

$|t| \le \sqrt{3}$

Khi đó $xy+yz+zx=\dfrac{1}{2}t^2-\dfrac{1}{2}$

$2P=t^2+2t-1=(t+1)^2-2 \ge -2$

$2P=(t-\sqrt{3})(t+2+\sqrt{3})+2+2\sqrt{3} \le 2+2\sqrt{3}$
 
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