If a = 6+2√3 , find the value of a - 1/a

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Solution

A = 6+2√3

1/a = 1/6+2√3

→ = 1/6+2√3 × 6-2√3/6-2√3

→ = (6-2√3)/(6+2√3)(6-2√3)

→ = (6-2√3)/(6²-(2√3)²)

→ = (6-2√3)/(36-4(3))

→ = (6-2√3)/(36-12)

→ = (6-2√3)/24

★a-1/a

→ 6+2√3 - (6-2√3)/24

→ {24(6+2√3) - 6 + 2√3}/24

→ {144+48√3-6+2√3}/24

→ {138+50√3}/24

→ 138/24 + 50√3/24

→ 23/4 + 25√3/12

→ {69+25√3}/12

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