If a=8+3√7 then find a+1/a

1.	If a=8+3√7 then find a+1/a
Answer» Answer: 16 given a=8+3√7 -(1) $\frac{1}{a} = \frac{1}{(8 + 3\sqrt{7}) } \times \frac{8 - 3\sqrt{7} }{(8 - 3 \sqrt{7} )}$ $\frac{1}{a} = \frac{8 - 3 \sqrt{7} }{( {8}^{2} ) - {(3 \sqrt{7 \: )} }^{2} } = \frac{8 - 3 \sqrt{7} }{64 - 63}$ $\frac{1}{a} =8 - 3 \sqrt{7 } \: \: \: \: \: \: \: - (2)$ $adding \: \: \: \: \: \: \: (1) \: \: \: and \: \: (2)$ $a + \frac{1}{a} = 8 + 3 \sqrt{7} + 8 - 3 \sqrt{7}$ $hence$ $a + \frac{1}{a} = 8 + 8 = 16$

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Answer:

given a=8+3√7 -(1)

$\frac{1}{a} = \frac{1}{(8 + 3\sqrt{7}) } \times \frac{8 - 3\sqrt{7} }{(8 - 3 \sqrt{7} )}$