IIT JEE , AIEEE Forum - Mathematics , Algebra

Conjurer

A good IIT level problem I should say.Olympiaders please be lenient ,might be damn easy for you.

If 4x^4 + 9y^4 =64

Then find the maximum value of x^2 + y^2.

I know a very nice way ,lets see who else can get this one.

sandy1990

4x⁴ + 9y⁴=64

did u mean this

Conjurer

Yes.Too lazy to type.

sandeepramesh

is the answer 10sqrt(2)/3 ?

Conjurer

Wrong.

elastiboysai

is d ans 4/3^{*[ ]}

13
2x^2/8=cos

3y^2/8=sin

x^2=4cos

y^2=8/3sin

now just maximise
4cos

+8/3sin

sandy1990

(x/2)⁴+(3)^1/2(y/2)⁴ =1

use sine /cosine

with this

and is it correct

10*2^1/2/3

elastiboysai

sandy,
conjurer has already said tht ans is wrong to rohit aka sandeepramesh

sandeepramesh

yes even i think that 10sqrt(2)/3 is right :)

elasti, how can both the angles be same? accord to urs sin^2a + cos^2a not = 1???

sandeepramesh

my method

to maximise the value, 4x^2 = 9y^2 and hence the result follows :)

elastiboysai

rohit see wat i have written clearly

elastiboysai

see once i assume 1 of dem = cos a, it immediately follows dat the oder is sina.
btw
y do u say maximise 4x^2=9y^2 ?

sandeepramesh

i mean for it to be maximised 4x^2 = 9y^2 is this wrong???

well i saw ur proof n it seems to be right :)

arpan1

@sandeep

even i did the same
that is for max both terms must b equal..

coolvignesh

hey guyz....
i think elastiboy is very much right.....
even it hought of the same method after seeing this problem...
js it was posted by elasti first...

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