IIT JEE , AIEEE Forum - Mathematics , Algebra

santosh05

given

a+b+c=3
find max value of a²b³c²

i thnk u hav to use am >gm principl

Sushmi

http://www.goiit.com/posts/list/algebra-if-x-y-z-6-then-find-max-value-of-x-2yz-41488.htm#203959

computer001

a spl method 4 this 1:
consider a/2 +a/2 +b/3 +b/3+b/3+c/2+c/2 =3

now fromAM-GM v no tht
{a/2 +a/2 +b/3 +b/3+b/3+c/2+c/2}/7> = {a^2/4*b^3/9*c^2/4}^1/7

so v have 3/7>={(a^2b^3c^2)^1/7}/{144}^1/7
taking 7th power
(3^7/7^7)*144>=a^2b^3c^2
so max value is 3^7*144/7^7

Conjurer

Are the no.s positive?

computer001

cummon mate...assume tht...
dun give the same post everywhere

Conjurer

Then you assume it, you are giving the answer isnt it?

AND PLZ WRITE COMPLETE QUESTIONS.

spideyunlimited

yup computer has used the correct method here. :)

santosh05

wat ll happn if u include negatve nos??????

spideyunlimited

computer001

if u incl neg nos the max value is infinity
as i can keep 1 value say b =1 and a->inf,c->-inf
but c^2 will tend to inf...
u will get max val->inf

priyesh

@computer u made a calc. error

its not 144 but 432 u forgot to multiply a 3 in denominator rest is fine

cheers!!!!!!!

Ask & Discuss Questions with Community & Experts