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if a=2 + sqrt3, then find the value of (...

if `a=2 + sqrt3`, then find the value of `(a-1/a)`.

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we have `a=2+ sqrt3`
then `1/a=1/(2+sqrt3)xx(2-sqrt3)/(2-sqrt3)` [ multiplying numerator and denominator by `(2-sqrt3)`]
`(2-sqrt3)/((2)^(2)-sqrt3)xx(2-sqrt3)/(4-3)=2-sqrt3 " " ["using identity", (a+b)(a-b)=a^(2)-b^(2)]`
`1/a =2-sqrt3`
`a-1/a=(2+sqrt3)-(2-sqrt3)=2+sqrt3-2+sqrt3=2sqrt3`
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