number system

It is given that m+1/m=2√3 . Find the value of each of the following.
(a)m^2+1/m^2
m+1/m=2√3
(m+1/m)^2 =(2√3)^2
m^2 + 1/m^2 + 2 = 12
m^2 + 1/m^2 = 10
(b)m-1/m
m^2 + 1/m^2 = 10
m^2 + 1/m^2 - 2 = 8
(m - 1/m)^2 = 8
m - 1/m = 2√2
(c)m^2-1/m^2
(m - 1/m)(m + 1/m) = m^2 - 1/m^2
(2√2)(2√3) = m^2 - 1/m^2
m^2 - 1/m^2 = 4√6

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2011-09-12 18:56:11 補充：
*CORRECTION:

(a), 2nd line should be:

(m+1/m)²=(2√3)²