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Algebra Level 4

The system of equations 4a4+36a2b2+9b4=20a2+30b21 4a^4+36a^2b^2+9b^4=20a^2+30b^2-1 2a3b+3ab3=5ab2a^3b+3ab^3=5ab has nn nonnegative (meaning both aa and bb are nonnegative) real solutions. Let these solutions be (a1,b1),(a2,b2),(an,bn)(a_1,b_1),(a_2,b_2),\cdots (a_n,b_n). The value of the sum i=1nai+bi\sum_{i=1}^n a_i+b_i can be expressed in the form a+bcd\dfrac{a+b\sqrt{c}}{d} where gcd(a,b,d)=1\gcd (a,b,d)=1 and cc is squarefree. Find a+b+c+da+b+c+d.

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