`\sqrt{3x^2 +12x+ 16} + \sqrt{y^2 -4y +13}= 5`
`+) \sqrt{3x^2+ 12x +16} = \sqrt{3(x^2 +4x+ 4) +4} = \sqrt{3(x +2)^2+ 4}`
` -> 3(x+ 2)^2 +4 \ge 4 -> \sqrt{3(x +2)^2+ 4} \ge \sqrt{4} = 2`
`+)\sqrt{y^2- 4y +13} = \sqrt{(y^2 -4y+ 4)+ 9}= \sqrt{(y -2)^2 +9}`
`-> (y -2)^2+ 9 \ge 9 -> \sqrt{(y- 2)^2 +9} \ge \sqrt{9}= 3`
`->\sqrt{3x^2 +12x+ 16} + \sqrt{y^2- 4y +13} \ge 2+ 3 = 5`
Dấu "=" xảy ra `\iff x+2=0;y -2 =0 \iff x=-2;y=2`