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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