Question

if a=6+2√3 then find the value of a-1/a

Answer 1

hey mate!!

$a = 6 + 2 \sqrt{3} \\ \\ \frac{1}{a} = \frac{1}{6 + 2 \sqrt{3} } \times \frac{6 - 2 \sqrt{3} }{6 - 2 \sqrt{3} } \\ \\ \frac{1}{a} = \frac{6 - 2 \sqrt{3} }{(6) {}^{2} - (2 \sqrt{3}) {}^{2} } \\ \\ \frac{1}{a} = \frac{6 - 2 \sqrt{3} }{36 - 12} \\ \\ \frac{1}{a} = \frac{6 - 2 \sqrt{3} }{24} \\ \\ \frac{1}{a} = \frac{2(3 - \sqrt{3}) }{24} \\ \\ \frac{1}{a} = \frac{3 - \sqrt{3} }{12} \\ \\ now \\ \\ a - \frac{1}{a} = 6 + 2 \sqrt{3} - \frac{3 - \sqrt{3} }{12} \\ \\ \frac{72 + 24 \sqrt{3} - 3 - \sqrt{3} }{12} \\ \\ \frac{69 + 23 \sqrt{3} }{12}$


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hope it helps

Answer 2

hope this helps you



brainiest please