Question

if a=6 + 2 root 3 find the value of a - 1 ÷ a

Answer 1

Here,
a=6+2√3

so,
a-1÷a=6+2√3-1÷6+2√3
=6+2√3-1/6+2√3
=5+2√3/6+2√3
=7

therefore,
a-1÷a=7 (when a=6+2√3)

Answer 2

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

i hope it helps you.