Question
Prove that:$\sqrt{\text{x}^{-1}\text{y}}\times\sqrt{\text{y}^{-1}\text{z}}\times\sqrt{\text{z}^{-1}\text{x}}=1.$
✓
Answer
$\text{L.H.S}=\sqrt{\text{x}^{-1}\text{y}}\times\sqrt{\text{y}^{-1}\text{z}}\times\sqrt{\text{z}^{-1}\text{x}}=1.$$=\sqrt{\frac{\text{y}}{\text{x}}}\times\sqrt{\frac{\text{z}}{\text{y}}}\times\sqrt{\frac{\text{x}}{\text{z}}}$
$=\sqrt{\frac{\text{y}}{\text{x}}\times\frac{\text{z}}{\text{y}}\times\frac{\text{x}}{\text{z}}}$
$=\sqrt1$
$=1$
$=\text{R.H.S}$
$=\sqrt{\frac{\text{y}}{\text{x}}\times\frac{\text{z}}{\text{y}}\times\frac{\text{x}}{\text{z}}}$
$=\sqrt1$
$=1$
$=\text{R.H.S}$
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