Question

IF a = 6+2 * root 3 , find the value of (a-1/a)

Answer 1

Answer:

(69 + 25√3) / 12

Solution:

We have ;

a = 6 + 2√3

Thus,

1/a = 1/(6+2√3)

Now,

Rationalising the denominator in RHS , we get ;

=> 1/a = (6 - 2√3) / (6 + 2√3)(6 - 2√3)

=> 1/a = (6 - 2√3) / {6²- (2√3)²}

=> 1/a = (6 - 2√3) / (36 - 12)

=> 1/a = (6 - 2√3) / 24

=> 1/a = 2(3 - √3) / 24

=> 1/a = (3 - √3) / 12

Now,

a - 1/a = 6 + 2√3 - (3 - √3) / 12

= [72 + 24√3 - (3 - √3)] / 12

= (72 + 24√3 - 3 + √3) / 12

= (69 + 25√3) / 12

Hence,

The required value of a + 1/a is :

(69 + 25√3) / 12

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.