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Show That: `{(X^(A-a^-1))^(1/(A-1))}^(A/(A+1))=X` - CBSE Class 9 - Mathematics

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Question

Show that:

`{(x^(a-a^-1))^(1/(a-1))}^(a/(a+1))=x`

Solution

`{(x^(a-a^-1))^(1/(a-1))}^(a/(a+1))=x`

LHS = `{(x^(a-a^-1))^(1/(a-1))}^(a/(a+1))`

`={(x^(a-1/a))^(1/(a-1)xxa/(a+1))}`

`={x^((a^2-1)/a)}^(a/(a^2-1))`

`=x^((a^2-1)/axxa/(a^2-1))`

`=x^1`

`= x`

= RHS

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 2: Exponents of Real Numbers
Ex. 2.20 | Q: 4.6 | Page no. 25

Video TutorialsVIEW ALL [1]

Solution Show That: `{(X^(A-a^-1))^(1/(A-1))}^(A/(A+1))=X` Concept: Laws of Exponents for Real Numbers.
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