Скачать или смотреть If x, y, z are positive real numbers, show that √(x^(-1) )y . √(y^(-1) )z . √(z^(-1) )x = 1 .

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...

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