Lagrange Multipliers/Systems of Equations: find the points on the ellipse x^2 + 2y^2=1 where f(x,y)= xy has its extreme values........Ive gotten three equations in terms of lambda, y , and x, but I cant solve the System, can anyone provide me with a walkthrough?

Question

anonymous · Answer

hmm

anonymous · Answer

this problem has my name in it, but can i solve it. I am very sleepy

anonymous · Answer

lets do this, i will help you solve for one variable, but then you well have to solve the rest, it will be easy because then you will only have to equations with only two unknown variables

anonymous · Answer

or maybe i will solve the whole thing

anonymous · Answer

what do you think?

anonymous · Answer

r u there? or did a robot ask this question?

anonymous · Answer

come on bud i dont want to solve this by myself

anonymous · Answer

srry

anonymous · Answer

was away for food

anonymous · Answer

man its 1:30 am in the morning i am so sleepy

anonymous · Answer

ya same here, i get...z=lambda
y=z2x
x=z4y

anonymous · Answer

and constraint
x^2 + y^2 = 1

anonymous · Answer

but cant get to the books answer

anonymous · Answer

whats books answer? i just wanna make sure i am doing the problem right

anonymous · Answer

$$(\pm (1/\sqrt{2}, 1/2), (\pm (1/\sqrt{2}, -1/2)$$

anonymous · Answer

plus or minus only belongs to the x coordinate
sorry

anonymous · Answer

(±1/2√,1/2),(±1/2√,−1/2)

anonymous · Answer

hmm, i get:

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