四川省初中數學競賽題：解方程x²+4x+13=√(81-x²)

x = sqrt(Im(1/2 sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))) - 1/2 sqrt(-76/3 - 409/(3 (4339 + 12 i sqrt(344382))^(1/3)) - 1/3 (4339 + 12 i sqrt(344382))^(1/3) + 8/sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3)))))^2 + (-2 + Re(1/2 sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))) - 1/2 sqrt(-76/3 - 409/(3 (4339 + 12 i sqrt(344382))^(1/3)) - 1/3 (4339 + 12 i sqrt(344382))^(1/3) + 8/sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))))))^2) (cos(-π + tan^(-1)(Im(1/2 sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))) - 1/2 sqrt(-76/3 - 409/(3 (4339 + 12 i sqrt(344382))^(1/3)) - 1/3 (4339 + 12 i sqrt(344382))^(1/3) + 8/sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3)))))/(-2 + Re(1/2 sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))) - 1/2 sqrt(-76/3 - 409/(3 (4339 + 12 i sqrt(344382))^(1/3)) - 1/3 (4339 + 12 i sqrt(344382))^(1/3) + 8/sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3)))))))) + i sin(-π + tan^(-1)(Im(1/2 sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))) - 1/2 sqrt(-76/3 - 409/(3 (4339 + 12 i sqrt(344382))^(1/3)) - 1/3 (4339 + 12 i sqrt(344382))^(1/3) + 8/sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3)))))/(-2 + Re(1/2 sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))) - 1/2 sqrt(-76/3 - 409/(3 (4339 + 12 i sqrt(344382))^(1/3)) - 1/3 (4339 + 12 i sqrt(344382))^(1/3) + 8/sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3)))))))))

x = sqrt(Im(1/2 sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))) + 1/2 sqrt(-76/3 - 409/(3 (4339 + 12 i sqrt(344382))^(1/3)) - 1/3 (4339 + 12 i sqrt(344382))^(1/3) + 8/sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3)))))^2 + (-2 + Re(1/2 sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))) + 1/2 sqrt(-76/3 - 409/(3 (4339 + 12 i sqrt(344382))^(1/3)) - 1/3 (4339 + 12 i sqrt(344382))^(1/3) + 8/sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))))))^2) (cos(π + tan^(-1)(Im(1/2 sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))) + 1/2 sqrt(-76/3 - 409/(3 (4339 + 12 i sqrt(344382))^(1/3)) - 1/3 (4339 + 12 i sqrt(344382))^(1/3) + 8/sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3)))))/(-2 + Re(1/2 sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))) + 1/2 sqrt(-76/3 - 409/(3 (4339 + 12 i sqrt(344382))^(1/3)) - 1/3 (4339 + 12 i sqrt(344382))^(1/3) + 8/sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3)))))))) + i sin(π + tan^(-1)(Im(1/2 sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))) + 1/2 sqrt(-76/3 - 409/(3 (4339 + 12 i sqrt(344382))^(1/3)) - 1/3 (4339 + 12 i sqrt(344382))^(1/3) + 8/sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3)))))/(-2 + Re(1/2 sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3))) + 1/2 sqrt(-76/3 - 409/(3 (4339 + 12 i sqrt(344382))^(1/3)) - 1/3 (4339 + 12 i sqrt(344382))^(1/3) + 8/sqrt(1/3 (-38 + 409/(4339 + 12 i sqrt(344382))^(1/3) + (4339 + 12 i sqrt(344382))^(1/3)))))))))