Hi freinds;

can someone give me the solution of #36 on GRE 8767?

I know how I should solve it but I cannot get the answer.

thank you

Hi freinds;

can someone give me the solution of #36 on GRE 8767?

I know how I should solve it but I cannot get the answer.

thank you

can someone give me the solution of #36 on GRE 8767?

I know how I should solve it but I cannot get the answer.

thank you

We're trying to minimize the function , subject to the restriction , which should immediately suggest the Lagrange multipliers method.

Of course, it's easier to work with . We can minimize this function, then take a square root. Then, letting , we set , so we have

We can quickly work out that the first two equations are satisfied when either or . But can never satisfy , so we must have , and thus and , so , and .

This is the "this is a timed test and we're in a hurry" version. I'm sure someone else could give a more lucid explanation.

Of course, it's easier to work with . We can minimize this function, then take a square root. Then, letting , we set , so we have

We can quickly work out that the first two equations are satisfied when either or . But can never satisfy , so we must have , and thus and , so , and .

This is the "this is a timed test and we're in a hurry" version. I'm sure someone else could give a more lucid explanation.

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