Given that ‘a’ is a root of the equation x2-x-3=0 then a3+1a5−a4−a3+a2  equals

a2−a−3=0a3+1=a+1a2−a+1a5−a4−a3+a2=a2a3−a2−a+1=a2a2a−1−a−1=a2a-1a2-1=a+1a3−a2it follows that a3+1a5−a4−a3+a2=a2−a+1a2−a2=432=49