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If a=b-sqrt(b^(2)-1), express b in terms...

If `a=b-sqrt(b^(2)-1)`, express b in terms of a.

A

`b=(1)/(2)(a^(-1)-a)`

B

`b=(1)/(2)(a+a^(-1))`

C

`b=(1)/(2)(a-a^(-1))`

D

`b=(-1)/(2)(a+a^(-1))`

Text Solution

Verified by Experts

The correct Answer is:
B
`a=b-sqrt(b^(2)-1)`
`implies sqrt(b^(2)-1)=b-aimpliesb^(2)-1=(b-a)^(2)`
`impliesb^(2)-1=b^(2)+a^(2)-2ab`
`implies2ab-1=a^(2)impliesa^(2)+1=2ab`
`implies(a^(2)+1)/(2a)=b`
`implies(1)/(2)(a+a^(-1))=b`
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  17. If a=b-sqrt(b^(2)-1), express b in terms of a.

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