Question 14
Let $a,b,c$ be the three real roots of the cubic equation
$$2x^3-4x^2-21x-8=0.$$
Given that
$$S=\frac1{ab+c-1}+\frac1{bc+a-1}+\frac1{ca+b-1}$$
is a rational number that can be expressed as a fraction in the lowest form $\frac mn$, find the value of $m^2+n^2$.
$$2x^3-4x^2-21x-8=0.$$
Given that
$$S=\frac1{ab+c-1}+\frac1{bc+a-1}+\frac1{ca+b-1}$$
is a rational number that can be expressed as a fraction in the lowest form $\frac mn$, find the value of $m^2+n^2$.