Here are two non calculus approaches to your problem:
Geometrically, denotes square of distance of the point from therefore,you have been asked to find the shortest distance between and the line in 2D space which is the perpendicular distance of 2x +3y=6 from (0,0) and which can be found from the formula
.Therefore answer should be
Another method:
Put where
Plugging in ,we get
Now r will be minimum when denominator will be maximum.
Also
Therefore,
and hence