Schur

Algebra Level 3

a3+b3+c3+abc5\large a^3 + b^3 + c^3 + abc \sqrt5 Given that a,ba,b and cc are the sides of a triangle with perimeter 3. If the minimum value of the expression above can be expressed as x+yx + \sqrt y for positive integers xx and yy, find the value of x+yx+ y.

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