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Find the indicated maximum or minimum value of f subject to the given constraint. ​Minimum: ​f(x,y)=2...

Find the indicated maximum or minimum value of f subject to the given constraint.

​Minimum: ​f(x,y)=2 x^2 + y ^2 + 2 xy + 3 x + 2 y​ ;  y^2 = x + 1

The minimum value is -------------.

(Type an integer or a simplified​ fraction.)

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