if x(sqr)+1/x(sqr) =a and x-1/x=b, where a and b are positive real, then minimum possible value which a/b can have,

A)2 root2 B) 2 C)root 2 D)4 plzz solve!!!!!!!!!!!!!!!!!!!!!!!!!

x² + 1/x² = a

(x - 1/x)² + 2 = a         ...............1

x-1/x = b

a/b = (x-1/x) + 2/(x-1/x)

put , x-1/x = t then

a/b = t + 2/t          .............2

 now dufferentiating this eq wrt t & putting it to 0 we get 

t = + or - root2

so , at t = root2 ,

 a/b =  root2 + 2/root2 = 2root2     

,this is the minimum value

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