If A and B are the two real values of kfor which the system of equations  x+2y+z=1,  x+3y+4z=k,  x+5y+10z=k2 is consistent, thenΑ+B=

Augmented matrix [AB]=1211134k1510102                                  R3−R1R2−R1~1211013k-1039k2-1                                      R3−3R2~ 1211013k-1000k2-3k+2   Since the system is consistent, we have  Rank Α=Rank [AB]k2−3  k+2=0     ⇒k=1,  2Α+B=    1+2=3