Question

√x^-1√y√y^-1√z√z^-1√x = 1

Answer 1

Question:

→ Prove this :

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

Answer:

→ 1 .

Step-by-step explanation:

We have an equation ,

$\sf \because { \sqrt{x} }^ { - 1} \times \sqrt{y} \times { \sqrt{y} }^{ - 1} \times \sqrt{z} \times { \sqrt{z} }^{ - 1} \times \sqrt{x} = 1. \\ \\ \sf \implies \frac{1}{ \sqrt{x} } \times \sqrt{y} \times \frac{1}{ \sqrt{y} } \times \sqrt{z} \times \frac{1}{ \sqrt{z} } \times \sqrt{x} = 1. \\ \\ \sf \implies \frac{1}{ \cancel{\sqrt{x} }} \times \cancel{\sqrt{x}} \times \cancel{\sqrt{y} } \times \frac{1}{ \cancel{\sqrt{y} }} \times \cancel{\sqrt{z} } \times \frac{1}{ \cancel{\sqrt{z} }} = 1. \\ \\ \sf \implies 1 \times 1 \times 1 = 1. \\ \\ \huge \boxed{ \pink{ \tt \therefore 1 = 1.}} \\ \\ \huge \orange{ \underline{ \mathbb{LHS = RHS }}}$

Hence, it is proved .

THANKS .

Answer 2

ANSWER

Step-by-step explanation:

$\begin{lgathered}\bf \because { \sqrt{x} }^ { - 1} \times \sqrt{y} \times { \sqrt{y} }^{ - 1} \times \sqrt{z} \times { \sqrt{z} }^{ - 1} \times \sqrt{x} = 1. \\ \\ \bf \implies \frac{1}{ \sqrt{x} } \times \sqrt{y} \times \frac{1}{ \sqrt{y} } \times \sqrt{z} \times \frac{1}{ \sqrt{z} } \times \sqrt{x} = 1. \\ \\ \bf \implies \frac{1}{ \cancel{\sqrt{x} }} \times \cancel{\sqrt{x}} \times \cancel{\sqrt{y} } \times \frac{1}{ \cancel{\sqrt{y} }} \times \cancel{\sqrt{z} } \times \frac{1}{ \cancel{\sqrt{z} }} = 1. \\ \\ \bf \implies 1 \times 1 \times 1 = 1.$

THANKS