Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

solve in R

solve in R

Last edited by tony123 (2007-10-01 21:46:39)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: solve in R

I don't know how to do it with legit pure math, but one answer is (4,9). 

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igloo myrtilles fourmis

tony123

Member

Registered: 2007-08-03

Posts: 229

Re: solve in R

(4,9).is the only answer but how

icy_A

Member

Registered: 2007-10-04

Posts: 5

Re: solve in R

Yes Your Right About The Answer Being (4,9) But I Also Do Not Know How Its (4,9).

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: solve in R

Rearrange it into 9(4/a + a) + (9/b + b) = 42, where a = √x and b = √y.

Now find min(4/a + a). You do this by differentiating and equating to 0.

(4/a+a)' = -4/a² + 1 = 0
-4/a² = -1
4 = a²
a = ±2.

But as a = √x and you can't get (real) negative roots, then a=2 (and thus x=4) is the minimising value.

For this, 9(4/a + a) = 36.

Following a similar procedure for the other half gives that min(9/b + b) = 6, when b=3 (and so y=9).

Adding these minimum values produces 42. As it's a minimum and there was only one solution do the differential equation in both cases, then (4,9) is the only solution that works. Any other (x,y) will give a greater answer.

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Why did the vector cross the road?
It wanted to be normal.