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If |z-4/z|=2 , then the maximum value of...

If `|z-4/z|=2` , then the maximum value of `|Z|` is equal to (1) `sqrt(3)+""1` (2) `sqrt(5)+""1` (3) 2 (4) `2""+sqrt(2)`

A

`sqrt3 + 1 `

B

` sqrt5 + 1 `

C

`2`

D

`2 + sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
B
`|Z|= |(Z-(4)/(Z))+(4)/(Z)|le|Z-(4)/(Z)|+(4)/(|Z|) le 2 + (4)/(|Z|)`
`rArr |Z|^(2) - 2 |Z| - 4 le 0`
`rArr [|z| - sqrt(5) + 1)][(Z| - 1(-sqrt(5))]le 0`
`rArr 0 le |Z| le sqrt(5) + 1`
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