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प्रश्न
Prove the following:
`sqrt(x^-1 y) · sqrt(y^-1 z) · sqrt(z^-1 x)` = 1
उत्तर
L.H.S.
= `sqrt(x^-1 y) · sqrt(y^-1 z) · sqrt(z^-1 x)`
= `sqrt(y/x) · sqrt(z/y) · sqrt(x/z)` .....(Using (am)n = amn)
= `sqrt((y/x)(z/y)(x/z))`
= `sqrt(x^(1-1) · y^(1-1) · z^(1-1))`
= `sqrt(x^° · y^° · z^°)`
= `sqrt(1·1·1)`
= 1 ......(Using a° = 1)
= R.H.S.
Hence proved.
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