MathDB

Let

a, b, c,

and

d

be real numbers that satisfy the system of equations \begin{align*} a+b&=-3\\ ab+bc+ca&= -4\\ abc+bcd+cda+dab&=14\\ abcd&=30. \end{align*} There exist relatively prime positive integers

m

and

n

such that

a^2 + b^2 + c^2 + d^2 = \frac{m}{n}.

Find

m + n

Problem Statement