Question

if $a,b,c$ are in $A.P$ as well in $G.P$., then find the value of $a^{b-c}+b^{c-a}+c^{a-b}$.

Answer 1

since a,b,c are in A.P and C.P

$\therefore$ let a,b,c$=[a-d,a,a+d]$

$\therefore a^2=a^2-d^2$

$($in C.P,$b^2=ac)$

$\therefore d=a^2-a^2=0$

$\therefore d=0$

$\therefore$ since $d=0$

$\therefore a=b=c$

value of the expression is $1+1+1=3$.