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प्रश्न
If a, b, c are positive real numbers, then \[\sqrt{a^{- 1} b} \times \sqrt{b^{- 1} c} \times \sqrt{c^{- 1} a}\] is equal to
पर्याय
1
abc
\[\sqrt{abc}\]
\[\frac{1}{abc}\]
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उत्तर
We have to find the value of `sqrt(a^-1b)xx sqrt (b^-1c) xx sqrt(c^-1 a)` when a, b, c are positive real numbers.
So,
`sqrt(a^-1b)xx sqrt (b^-1c) xx sqrt(c^-1 a) =sqrt(1/a xxb)xx sqrt(1/b xx c) xx sqrt(1/c xx a)`
`sqrt(b/a) xx sqrt (c/b) xx sqrt(a/c)`
Taking square root as common we get
\[\sqrt{a^{- 1} b} \times \sqrt{b^{- 1} c} \times \sqrt{c^{- 1} a} = \sqrt{\frac{b}{a} \times \frac{c}{b} \times \frac{a}{c}}\]
\[\sqrt{a^{- 1} b} \times \sqrt{b^{- 1} c} \times \sqrt{c^{- 1} a} = 1\]
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