# More Difficult System of Equations

Solve the following system of equations:

$a + b + c + \sqrt{d} = 2241.000000000000 \\ a + b + \sqrt{c} + d = 1300.208973068654 \\ a + \sqrt{b} + c + d = 1590.057628441591 \\ \sqrt{a} + b + c + d = 1681.207436873820$

Report your answer as $$\left(2^{10}\right)^3 a+\left(2^{10}\right)^2 b+2^{10} c+d$$

Details:

• $$a,b,c,d$$ are positive integers not more than $$2^{10}$$

• Only the first 16 digits of the exact values have been given in the RHS.

• I have generated the values of $$a,b,c,d$$ at random.

Inspired by: Difficult system of Equations

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