Question

If xyz are real numbers prove that √(x^(-1) )y . √(y^(-1) )z . √(z^(-1) )x = 1

Answer 1

This is the solution to your question

Answer 2

Answer:

We have to prove that,

$\sqrt{(x^{-1})y}.\sqrt{(y^{-1})z} .\sqrt{(z^{-1})x} = 1$

L.H.S.

$\sqrt{(x^{-1})y}.\sqrt{(y^{-1})z} .\sqrt{(z^{-1})x}$

$=\sqrt{x^{-1}y}.\sqrt{y^{-1}z} .\sqrt{z^{-1}x}$

$=\sqrt{x^{-1}y.y^{-1}z.z^{-1}x}$     $(\sqrt{a}\times \sqrt{b}=\sqrt{ab})$

$=\sqrt{x^{-1+1}.y^{-1+1}z^{-1+1}}$      $(a^m\times a^n=a^{m+n})$

$=\sqrt{x^0 y^0 z^0}$      

$=\sqrt{1\times 1\times 1}$

$=\sqrt{1}$

$=1$

= R.H.S.

Hence, proved...