use Lagrange multipliers to find the max and min of f(x,y) =x^2+y^2 subject to xy=1. Help please

Question

anonymous · Answer

I got lamda = +-2. and stuck.

amistre64 · Answer

what process got you to L=+-2 ?

anonymous · Answer

take del F = lamda *del g. it's <2x,2y> = lamda

anonymous · Answer

so, 2x = lamda y --> x = lamda y/2
2y =lamda x ---> y = lamda x/2 
time them xy =1 = lamda^2 /4 --> lamda = +-2

amistre64 · Answer

Fx = 2x , LGx = Ly

x = Ly/2

Fy = 2y ,  LGy = Lx

y = Lx/2

and we know that xy = 1

L^2 xy/4 = 1

L^2 xy = 4

since xy=1, L = +- 2  does seem appropriate :)   so far

anonymous · Answer

and then? I stuck.

amistre64 · Answer

x = y;  y = x

or 

x = -y;  y = -x

would be our possible outcomes for L = +- 2

if x=y then we can say x^2 = 1

if y=-x , does -x^2 = 1 exist?

anonymous · Answer

how x =-y? I got x =y but x cannot be -y

amistre64 · Answer

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