Question

if a=9+4√5, find the value of (a+1/a)

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Answer 1

Answer:

Here in the second step i took LCM.. So dont get confused.. Have a good day

Answer 2

Answer:

18

Step-by-step explanation:

$\frac{1}{a} = \frac{1}{9 + 4 \sqrt{5} } = \frac{1}{9 + 4 \sqrt{5} } \times \frac{9 - 4 \sqrt{5} }{9 - 4 \sqrt{5} } = \frac{9 - 4 \sqrt{5} }{ {9}^{2} - {(4 \sqrt{5)} }^{2} } = \frac{9 - 4 \sqrt{5} }{81 - 80} = 9 - 4 \sqrt{5}$

Now,

$a + \frac{1}{a} = 9 + 4 \sqrt{5} + 9 - 4 \sqrt{5 } = 18$

That's it.