`A(1;-1), B(3;2)`
`text{Vì M thuộc Oy}` nên gọi `M(0;y)`
Ta có:
`\vec{MA}=(1;-1-y)`
`=>MA^2=1^2+(-1-y)^2=y^2+2y+2`
`\vec{MB}=(3;2-y)`
`=>MB^2=3^2+(2-y)^2=y^2-4y+13`
`=>MA^2+MB^2=2y^2-2y+15`
`=2(y^2-2y. 1/ 2 + 1/ 4)+{29}/2=2(y- 1/ 2)^2 +{29}/ 2≥{29}/2 ∀y` `(vì (y- 1/ 2)^2≥0 ∀y)`
Dấu "=" xảy ra khi `y- 1/ 2=0<=>y= 1/ 2`
`=>M(0; 1/ 2)`
Vậy khi `M(0; 1/ 2)` thì `MA^2+MB^2` có $GTNN$ `={29}/2`