Question

If a=6+2√3 find a-1÷a
plz answer fast​

Answer 1

Answer:

$a-\frac{1}{a}=\frac{69+25\sqrt{3}}{12}$

Step-by-step explanation:

$Given \: a = 6+2\sqrt{3}\:--(1)$

$\frac{1}{a}\\= \frac{1}{6+2\sqrt{3}}\\=\frac{6-2\sqrt{3}}{(6+2\sqrt{3})(6-2\sqrt{3})}\\=\frac{6-2\sqrt{3}}{6^{2}-(2\sqrt{3})^{2}}\\=\frac{6-2\sqrt{3}}{36-12}\\=\frac{2(3-\sqrt{3})}{24}\\=\frac{(3-\sqrt{3})}{12}\:---(2)$

$a-\frac{1}{a}\\=6+2\sqrt{3}-\frac{(3-\sqrt{3})}{12}\\=\frac{12(6+2\sqrt{3})-(3-\sqrt{3})}{12}\\=\frac{72+24\sqrt{3}-3+\sqrt{3}}{12}\\=\frac{69+25\sqrt{3}}{12}$

Therefore,

$a-\frac{1}{a}=\frac{69+25\sqrt{3}}{12}$

•••♪

Answer 2

$\huge\sf{Answer:-}$

$\sf a = 6 + 2 \sqrt{3} - eq(1) \\ \sf = \frac{1}{a} \\ \sf = \frac{1}{6 + 2 \sqrt{3} }$

$\sf = \frac{6 - 2 \sqrt{3} }{(6 + 2 \sqrt{3}) - (6 - 2 \sqrt{3}) }$

= 6 - 2 √3 / 6² - (2 √3)²

= 6 - 2 √3 / 6² - (2 √3)²= 6 - 2 √3 / 36 - 12

$\sf = \frac{6 - 2 \sqrt{3} }{63 - 12} \\ \sf = \frac{(3 - \sqrt{3}) }{12} - eq(2) \\ \sf = a - \frac{1}{a} \\ \sf = 6 + 2 \sqrt{3} - \frac{(3 - \sqrt{3}) }{12} \\ \sf = \frac{612(6 + 2 \sqrt{3) }- (3 - \sqrt{3)} }{12} \\ \sf = \frac{69 + 25 \sqrt{3} }{12}$

So,

$\sf = > a - \frac{1}{a} \\ \sf = > \frac{69 + 25 \sqrt{3} }{12}$

$\sf\color{red}{Nayan}$$\sf\color{blue}{Shreyas ....}$