# More Difficult System of Equations

**Computer Science**Level 5

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