Double Simplicity

Algebra Level 5

Let x,y x,y be real numbers such that x2+xy+2y2=8 x^2 + xy + 2y^2 = 8 .

The greatest value that x+y x + y can attain is a real number equal to abb \dfrac{a\sqrt{b}}{b} , where a,b a,b are positive integers such that b b does not divide a a , and b b is square- free.

Evaluate a+b a+b .

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