Let q be a real number. Gugu has a napkin with ten distinct real numbers written on it, and he writes the following three lines of real numbers on the blackboard:[*]In the first line, Gugu writes down every number of the form a−b, where a and b are two (not necessarily distinct) numbers on his napkin.
[*]In the second line, Gugu writes down every number of the form qab, where a and b are
two (not necessarily distinct) numbers from the first line.
[*]In the third line, Gugu writes down every number of the form a2+b2−c2−d2, where a,b,c,d are four (not necessarily distinct) numbers from the first line.Determine all values of q such that, regardless of the numbers on Gugu's napkin, every number in the second line is also a number in the third line. algebraIMO ShortlistIMO Shortlist 2017