The set of all possible values of in the interval (0, ) for which the points (1,2) and ( , ) lie on the same side of the line x+y=1 , is .

Step-by-step solution

for lying on the same side ( + -1)(1+2-1)>0 aligned & + >1 & 1 2 + 1 2 > 1 2 aligned aligned & ( + 4 )> 1 2 & 4 < + 4 < 3 4 & 0 < < 2 aligned