If x = yz , y = zx and z = xy , then(a) \(\frac{xy}{z} = 1\)(b) xyz =

1.	If x = yz , y = zx and z = xy , then(a) \(\frac{xy}{z} = 1\)(b) xyz = 1 (c) x + y + z = 1 (d) xz = y
Answer» (b) xyz = 1 z = x^y = (y^z)^y (∵ x = y^z ) = y^zy = (z^x)^zy = z^xyz (∵ y = z^x) ∴ z¹ = z^xyz ⇒ xyz = 1

If x = yz , y = zx and z = xy , then(a) \(\frac{xy}{z} = 1\)(b) xyz = 1 (c) x + y + z = 1 (d) xz = y

Answer»

(b) xyz = 1

z = x^y = (y^z)^y (∵ x = y^z )

= y^zy = (z^x)^zy = z^xyz (∵ y = z^x)

∴ z¹ = z^xyz ⇒ xyz = 1