prove that a+b+2c a b c b+c+2a b = 2( a+b+c)3 c a c+a+2b Share with your friends Share 5 Vijay Kumar Gupta answered this Consider the following determinant. a+b+2cabcb+c+2abcac+a+2bApply the column operation, C1→ C1+ C2+ C3 to get, =2a+b+cab2a+b+c b+c+2ab2a+b+ca c+a+2bTake 2a+b+c out from C1 =2a+b+c 1ab1 b+c+2ab1a c+a+2bApply the row operations, R2→R2-R1, R3→R3-R1 to get, =2a+b+c 1ab0 a+b+c000 a+b+cTake out a+b+c from R2 and R3 =2a+b+ca+b+ca+b+c 1ab0 1000 1 =2a+b+c3 1ab0 1000 1Expand along C1 to get, =2a+b+c3 1×1×1-0×0 =2a+b+c3 1-0 =2a+b+c3Thus, it is proved that, a+b+2cabcb+c+2abcac+a+2b= 2a+b+c3 14 View Full Answer
