Question

If x, y, z are real number, then show that √x-1y,√y-1z,√z-1x=1

Answer 1

Given:  x, y, z are real number.

To find:  Show that √(x^-1)y . √(y^-1)z . √(z^-1)x = 1

Solution:

• Now we have given the expression √(x^-1)y . √(y^-1)z . √(z^-1)x = 1.

• Lets consider LHS first, we have:

           √(x^-1)y . √(y^-1)z . √(z^-1)x

• It can be rewritten as :

           √y/x . √z/y . √x/z

• Now multiplying all three, we get:

          √ y/x . z/y . x/z

         √xyz / xyz

         √1 = 1 ....................RHS.

• Hence LHS = RHS.

Answer:

       So from above solution we proved that √(x^-1)y . √(y^-1)z . √(z^-1)x = 1