If ax=√b, by=√c and cz=√a, find the value of xyz.
Answer:
18
- Let's write ax=√b as:
ax=b12⟹a2x=b
and
by=√c⟹by=c12⟹b2y=c
and
cz=√a⟹cz=a12⟹c2z=a - Put the value of c in c2z=a
⟹a=(b2y)2z⟹a=b2×2×yz⟹a=b4yz
Now put the value of b
a=(a2x)4yz⟹a=a2×4×xyz⟹a1=a8xyz - On comparing powers in above equation,
⟹1=8xyz⟹xyz=18 - Therefore, the value of xyz is 18.