Question

If $a,b,c$ are in A.P. and $(a+2b-c)(4b+2c-2a)(c+a-b)=\lambda$ abc, then find the value of $\lambda$.

Answer 1

Answer: 8

Let $a=A-d$
$b=A$
$c=A+d$
$\therefore (2A-2d)(4A+4d)(A)=\lambda (A-d)A(A+d)$
$\text{ Hence, }\lambda =8$