Question

what is the maximum value for
\[4/(4-x^2) + 9/(9-y^2)\]
given that both \[x,y \in (-2,2)\]
and xy=-1

Answer 1

Use lagrange multipliers

Answer 2

U know how to diffrentiate right

Answer 3

thats so very cool!
thanx buddy..never knew about this..
and yes,,i know how to differentiaite..

Answer 4

differentiate*

Answer 5

leme try to solve here..

Answer 6

g(x,y) = xy+1
f(x,y) = 4/(4-x^2) + 9/(9-y^2)
q(x,y,k) = f(x,y) + k(g(x,y)) = 4/(4-x^2) + 9/(9-y^2) + kxy + k
dq/dx = 4(2x)/(4-x^2)^2 + ky
dq/dy = 9(2y)/(9-y^2)^2 + kx
dq/dk = xy + 1
on equating each to 0 ,
dont you think it'll be quite tedius to solve for x,y and k from here?

Answer 7

it gives quartic eqn in x and y.. it'll require to first convert it into cubic eqn by subsn,,then solve that eqn by converting to depressed eqn and make more substn..sir,,this is just a 4 mark objective ques..there has to be a simpler way..

Answer 8

Dude g(x)=xy+1
del(f)=k.del(g)
g=1
will give 3 equationa and 3 unknowns

Answer 9

didnt get you..

Answer 10

\[\frac{df}{dx}i+\frac{df}{dy}j=\lambda[\frac{dg}{dx}i+\frac{dg}{dy}j]\]
and
\[xy=-1\]

Answer 11

i solve it and got the answer

Answer 12

whats the ans?

Answer 13

x=sqrt[29/21] and -sqrt[29/21]

Answer 14

find y accodingly