Question

If p=q^r , p= r^p, and r= p^q , prove that : pqr=1​

Answer 1

Answer:

Arrange a combined equation with exponent as ‘pqr’

We have

p = q^r … (1)

q = r^p … (2)

r = p^q … (3)

substituting equation (2) in equation (1)

ie., p = (r^p)^r … (4)

substituting equation (3) inside the bracket of equation (4)

ie., p = ((p^q)^p)^r … (5)

Using the identity (a^m)^n = a^mn we can write

p = p^qpr … (6)

In order to satisfy the equality of the equation (6), the exponent qpr must be 1.

ie., p = p^1 or p =p