Question

If a,b,c are in AP whereas x,y,z are in GP , what is the value of $x^b-c$ . $y^c-a$ . $z^a-b$?

• A. 1
• B. x
• C. Cannot be determined

Answer 1

The correct option is A 1

If a,b,c are in AP
Hence 2b=a+c
And x,y,z in GP
Lets assume, common ratio is P, so y=xP and $z=x{P}^2$
So,
$x^{(b-c)}.y^{(c-a)}.z^{(a-b)}=x^{(b-c)}.(xP{)}^{(c-a)}.(x{P}^2{)}^{(a-b)}=x^{(b-c)}.x^{(c-a)}.P^{(c-a)}.x^{(a-b)}.P^{(2a-2b)}=x^a.P^{(c+a-2b)}=x^a.P^{(2b-2b)}=x^0.P^0=1$