Question

How do I go about solving this? Yet another difficult, but interesting question. Question ENCL

Answer 1

@Hero
@amistre64
@radar
@mathstudent55

Answer 2

min max brings to mind derivatives

let f=(a+b)c and ng=n(a^2+b^2+c^2-1)

fa = c nga = n 2a
fb = c ngb = n 2b
fc = a+b ngc = n 2c

when f, = ng, we have a max/min condition if my idea is going correctly

Answer 3

a+b = 2nc; n=(a+b)/2c

c = 2n b
= b(a+b)/c

c^2 = b(a+b)

c = 2n a
=a(a+b)/c

c^2 = a(a+b)

a(a+b) = b(a+b) when a/b = 1; hence when a=b

c^2 = b(b+b) = 2b^2

therefore: assuming all positive values for a,b,c

b^2 + b^2 +2b^2 = 1

4b^2 = 1

b^2 = 1/4, b=1/2

a=1/2, b=1/2, c=sqrt(2)/2

is my rough idea

Answer 4

or does f=(a+b)^c ?? since thats an odd place to place the c for multiplication ... not unheard of, but just odd in general

Answer 5

langrange multipliers is what my idea was trying to recall :)

Answer 6

im guessing this means the wolf agrees

http://www.wolframalpha.com/input/?i=maximize+%28a%2Bb%29*c%2C+given+that+a%5E2%2Bb%5E2%2Bc%5E2%3D1

Answer 7

@amistre64 Can you explain a little?

Answer 8

i explained alot ... what else is there :)

Answer 9

ng ?

Answer 10

theres not lambda key .... and lambda is just sume multiplier to g

Answer 11

g = a^2 + b^2 + c^2 - 1 ?

Answer 12

in lagrange multipliers; we have a setup that is constrained;

in this case: f is constrained by g

f = (a+b)c and g is the sphere of radius 1 centered at the origin

Answer 13

Is this Multivar. Calc?

Answer 14

yes

Answer 15

No other way to do this?

Answer 16

prolly, but you didnt specify a method

Answer 17

Okay, I think this is good enough.
I am not very well-versed in Multi.-Vari. Calc. I'll see what i can do about that.
Thanks! :)

Answer 18

when the gradient of f and g are equal there is a min max relationship involved. which is what the lagrange multipler method is about

Answer 19

@ganeshie8 ?
Can you explain this a little?
I don't know multi var calc.

Answer 20

@BSwan wana try this using number theory ? :)

Answer 21

why he thinks its multi var calc. ?!

Answer 22

Because the answer is amistre64 provided was purely multi var. calc.

Answer 23

multi var calc gave the answer already : amistre's solution was using lagrange multipliers

Answer 24

Akash wants to do this without calculus i think...

Answer 25

Yeah.

Answer 26

yes we want to optimize the value of (a+b)c over a sphere

Answer 27

ok let me think , number theory dnt help with real number

Answer 28

unless it said (a+b)c integer
which is not given

Answer 29

yeah, max value of (a+b)c is is 1/sqrt(2)

http://www.wolframalpha.com/input/?i=maximize+%28a%2Bb%29*c%2C+given+that+a%5E2%2Bb%5E2%2Bc%5E2%3D1

Answer 30

so i think we may have to try completing the square or some other tricks and look for upper bound

Answer 31

mmm ill think of dump method :D