If ax = (x + y + z)y , ay = (x + y + z)z , az = (x + y + z)x , then:(a

1.	If ax = (x + y + z)y , ay = (x + y + z)z , az = (x + y + z)x , then:(a) 3(x + y + z) = a (b) 2a = x + y + z (c) x + y + z = 0 (d) x = y = z = a/3
Answer» (d) \(\frac{a}{3}.\) a^x . a^y . a^z = (x + y + z)^{x + y + z} ⇒ a^{x + y + z} = (x + y + z)^{x + y + z} ⇒ a = (x + y + z) Now, (x + y + z)^y = a^x (given) ⇒ (x + y + z)^y = (x + y + z)^x ⇒ y = x Similarly, y = z and z = x. ∴ x = y = z = \(\frac{x+y+z}{3}\) = \(\frac{a}{3}.\)

If ax = (x + y + z)y , ay = (x + y + z)z , az = (x + y + z)x , then:(a) 3(x + y + z) = a (b) 2a = x + y + z (c) x + y + z = 0 (d) x = y = z = a/3

Answer»

(d) \(\frac{a}{3}.\)

a^x . a^y . a^z = (x + y + z)^{x + y + z}

⇒ a^{x + y + z} = (x + y + z)^{x + y + z}

⇒ a = (x + y + z)

Now, (x + y + z)^y = a^x (given)

⇒ (x + y + z)^y = (x + y + z)^x ⇒ y = x

Similarly, y = z and z = x.

∴ x = y = z = \(\frac{x+y+z}{3}\) = \(\frac{a}{3}.\)