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a=9-4sqrt(5) ,sqrt(a)-1/sqrt(a)=?...

`a=9-4sqrt(5)` ,`sqrt(a)-1/sqrt(a)=?`

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We have, `a=9-4sqrt(5)` . . .(1)
`:." "(1)/(a)=(1)/(9-4sqrt(5))=(1)/(9-4sqrt(5))xx(9+4sqrt(5))/(9+4sqrt(5))=(9+4sqrt(5))/((9)^(2)-(4sqrt(5))^(2))=(9+4sqrt(5))/(81-80)=9+4sqrt(5)` . . . (2)
`"Now, "(sqrt(a)-(1)/(sqrt(a)))^(2)=a+(1)/(a)-2sqrt(a).(1)/(sqrt(a))=a+(1)/(a)-2(9-4sqrt(5))+(9+4sqrt(5))+(9+4sqrt(5))-2`
`rArr" "(sqrt(a)-(1)/(sqrt(a)))^(2)=16`
Taking square root on both sides
`:." "sqrt(a)-(1)/(sqrt(a))=+-sqrt(16)" "rArr" "sqrt(a)=(1)/(sqrt(a))=+-4`
`"But since "alt(1)/(a)" "rArr" "sqrt(a)lt(1)/(sqrt(a))`
`rArr" "sqrt(a)-(1)/(sqrt(a))lt0`
`:." "sqrt(a)-(1)/(sqrt(a))=-4`
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