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If $\big|z-\large\frac{4}{z}\big|$$=2$,the maximum value of $\mid z\mid$ is equal to

(A) $\;\sqrt 3-1$

(B) $\;\sqrt 3+1$

(C) $\;\sqrt 5+1$

(D) $\;1$

Can you answer this question?
 
 

1 Answer

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$\mid z\mid-\large\frac{4}{\mid z\mid}$$\leq \big|\mid z\mid-\large\frac{4}{\mid z\mid}\big|$$=2$
$\Rightarrow \mid z\mid^2-2\mid z\mid-4\leq 0$
$\Rightarrow (\mid z\mid-1\mid)^2\leq 5$
$\Rightarrow \mid z\mid\leq \sqrt 5+1$
$\Rightarrow $Maximum value of $\mid z\mid$ is $\sqrt 5+1$
Hence (C) is the correct answer.
answered Apr 9, 2014 by sreemathi.v
 

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