Substituting these results into the original equation, B + sqrt(CA) = 31,

after much algebra gives:153k^{4} - 1017k^{3} +1798k^{2} 994k + 56 = 0

which factorises to (3k 4)(51k^{3} -271k^{2} + 238k 14) = 0.

The linear factor yields k = 4/3 which gives the integer solution already posted, while the cubic factor gives three irrational roots, two of which give values of A, B and C that satisfy the original problem, as follows: