The number of integers a in the interval [1,2014] for which the system of equations x+y=a x² x-1 + y² y-1 =4 has finitely many solutions is

Step-by-step solution

x²-1+1 x-1 + y²-1+1 y-1 =4x+1+ 1 x-1 +y+1+ 1 y-1 =4a+2+ 1 x-1 + 1 (a-1)-x =4 (a-1)-x+x-1 (x-1)[(a-1)-x] =2-a a 2[ for a=2 equation have infinitely many solution] (x-1)[(a-1)-x]=-1(x-1)[x-(a-1)]=1x²-a x+(a-2)=0D>0 equation have 2 real roots so an be 1,3,4 .2014 a can be 1,3,4 .2014 ans 2013