Question

If a=6+2√3 find the value of a-1/a

Answer 1

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

hope it helps....

#snehitha2

★brainly benefactor★

Answer 2

Answer:

$a-\frac{1}{a}=\frac{69+25\sqrt3}{12}$          

Step-by-step explanation:

Given : $a=6+2\sqrt3$

To find : The value of $a-\frac{1}{a}$

Solution :

First we find, $\frac{1}{a}$ where $a=6+2\sqrt3$

$\frac{1}{a}=\frac{1}{6+2\sqrt3}$

Rationalize,

$\frac{1}{a}=\frac{1}{6+2\sqrt3}\times \frac{6-2\sqrt3}{6-2\sqrt3}$

$\frac{1}{a}=\frac{6-2\sqrt3}{6^2-(2\sqrt3)^2}$

$\frac{1}{a}=\frac{6-2\sqrt3}{36-4\times 3}$

$\frac{1}{a}=\frac{6-2\sqrt3}{36-12}$

$\frac{1}{a}=\frac{2(3-\sqrt3)}{24}$

$\frac{1}{a}=\frac{3-\sqrt3}{12}$

Expression $a-\frac{1}{a}$ substitute the values,

$a-\frac{1}{a}=6+2\sqrt3-\frac{3-\sqrt3}{12}$

$a-\frac{1}{a}=\frac{12(6+2\sqrt3)-(3-\sqrt3)}{12}$

$a-\frac{1}{a}=\frac{72+24\sqrt3-3+\sqrt3}{12}$

$a-\frac{1}{a}=\frac{69+25\sqrt3}{12}$

Therefore, $a-\frac{1}{a}=\frac{69+25\sqrt3}{12}$