# Is something sketchy going on here?

Algebra Level 4

The system of equations $4a^4+36a^2b^2+9b^4=20a^2+30b^2-1$ $2a^3b+3ab^3=5ab$ has $$n$$ nonnegative (meaning both $$a$$ and $$b$$ are nonnegative) real solutions. Let these solutions be $$(a_1,b_1),(a_2,b_2),\cdots (a_n,b_n)$$. The value of the sum $\sum_{i=1}^n a_i+b_i$ can be expressed in the form $$\dfrac{a+b\sqrt{c}}{d}$$ where $$\gcd (a,b,d)=1$$ and $$c$$ is squarefree. Find $$a+b+c+d$$.

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