Question

if a =6+2√3 ,find a-1/a​

Answer 1

Answer:

69+25root3/12

Step-by-step explanation:

Hope it helps you

Answer 2

Answer:

$a = 6 + 2 \sqrt{3} \\ \frac{1}{a } = \frac{1}{6 + 2 \sqrt{3} } \times \frac{6 - 2 \sqrt{3} }{6 - 2 \sqrt{3} } \\ \: \: \: \: = \frac{6 - 2 \sqrt{3} }{6 {}^{2} - (2 \sqrt{3} ) {}^{2} } = \frac{6 - 2 \sqrt{3} }{36 - 12} \\ \: {} \: \: \: \: = \frac{6 - 2 \sqrt{3} }{24} = \frac{6}{24} - \frac{2 \sqrt{3} }{24} \\ \: \: \: \frac{1}{a} \: \: = \frac{6 - 2 \sqrt{3} }{24} \\ a - \frac{1}{a} = 6 + 2 \sqrt{3} - \frac{6 - 2 \sqrt{3} }{24} \\ \: \: \: \: \: \: \: \: \: \: \: \: = \frac{144 + 48 \sqrt{3} - 6 - 2 \sqrt{3} }{24} \\ \: \: \: \: \: \: \: \: \: \: \: = \frac{138 + 46 \sqrt{3} }{24}$