Quadratic eqn w/ 2 var's: for x^2-xy+2y^2=1, find highest, lowest values of x^2+2y^2

[Zulgok]

I have to find the lowest and highest value of x² + 2y² when:

x² - xy + 2y² = 1

What I tried doing with it :

x² - (y)x + (2y² - 1) = 0

Discriminant = -7y² + 4

But I'm not really sure what I could do next. A hint would be appreciated.

 

[pka]

I have to find the lowest and highest value of x² + 2y² when:

x² - xy + 2y² = 1

What I tried doing with it :

x² - (y)x + (2y² - 1) = 0

Discriminant = -7y² + 4

But I'm not really sure what I could do next. A hint would be appreciated.

Here is the plot.

 

[Deleted member 4993]

I have to find the lowest and highest value of x² + 2y² when:

x² - xy + 2y² = 1

What I tried doing with it :

x² - (y)x + (2y² - 1) = 0

Discriminant = -7y² + 4

But I'm not really sure what I could do next. A hint would be appreciated.

Have you studied Lagrange Indeterminate multiplier method?

 

[Zulgok]

Have you studied Lagrange Indeterminate multiplier method?

No, I haven't.