please solve these two questions
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2.) a = 2+√3
a-(1/a)=(a^2 -1)/a (1)
a^2 = 2^2 + 2*(2*√3) +(√3)^2
=4+4√3+3
=7+4√3
so now putting this in (1)
a-(1/a)=((7+4√3) -1) / (2+√3)
=(6+4√3) / 2+√3
Multiplying numerator and denominator by 2-√3,
a-(1/a)= (6+4√3)*(2-√3) / (2+√3)*(2-√3)
=(12 - 6√3 + 8√3 - 12 ) / (4 - 3)
So, a-(1/a)= 2√3
a-(1/a)=(a^2 -1)/a (1)
a^2 = 2^2 + 2*(2*√3) +(√3)^2
=4+4√3+3
=7+4√3
so now putting this in (1)
a-(1/a)=((7+4√3) -1) / (2+√3)
=(6+4√3) / 2+√3
Multiplying numerator and denominator by 2-√3,
a-(1/a)= (6+4√3)*(2-√3) / (2+√3)*(2-√3)
=(12 - 6√3 + 8√3 - 12 ) / (4 - 3)
So, a-(1/a)= 2√3
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