Question

if x,y,z are real numbers show that ✔x ^-1 z multiply ✔y ^-1 z multiply ✔z ^-1 x = 1
✔ is underroot
I can't understand help​

Answer 1

Hey Pretty Stranger!

$\bf \: Correct \: Question :$

If x,y,z are real numbers show that :

$\sf \: \sqrt{ {x}^{ - 1}y } \times \sqrt{ {y}^{ - 1} z} \times \sqrt{ {z}^{ - 1} x} = 1$

$\bf \: Solution :$

We've :

$\rightarrow \sf \: \sqrt{ {x}^{ - 1}y } \times \sqrt{ {y}^{ - 1} z} \times \sqrt{ {z}^{ - 1} x}$

$\rightarrow \sf \: \sqrt{ \dfrac{y}{x} } \times \sqrt{ \dfrac{z}{y} } \times \sqrt{ \dfrac{x}{z} }$

$\rightarrow \sf \: ({ \dfrac{y}{x} })^{ \frac{1}{2} } \: \: ( { \dfrac{z}{y} })^{ \frac{1}{2} } \: \: ( { \dfrac{x}{z} })^{ \frac{1}{2} }$

$\rightarrow \sf \: \dfrac{ {y}^{ \frac{1}{2} } }{ {x}^{ \frac{1}{2} } } \times \dfrac{ {z}^{ \frac{1}{2} } }{ {y}^{ \frac{1}{2} } } \times \dfrac{ {x}^{ \frac{1}{2} } }{ {z}^{ \frac{1}{2} } }$

$\rightarrow \sf \: 1$

Hence, Proved!