Find the smallest possible value of the quantity under the restriction that

How would I go about solving this? Please help.

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- Sep 19th 2008, 02:54 PMlightningstab714Quadratic Equations
Find the smallest possible value of the quantity under the restriction that

How would I go about solving this? Please help. - Sep 19th 2008, 02:58 PMmr fantastic
- Sep 19th 2008, 03:24 PMlightningstab714
Thanks.

- Sep 19th 2008, 07:14 PMpankaj
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