Question

if a=5+2√6, then find the value of
i) a+(1/a)​

Answer 1

Question:

If a = 5+2√6, then find the value of $\sf {a+ \dfrac{1}{a}}$

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Solution:

We are given the value of a as 5+2√6.

First, we have to find the value of $\sf \dfrac{1}{a}$

$\sf \dfrac{1}{a}$ = $\sf \dfrac{1}{5+2\sqrt{6} }$

Rationalizing the denominator:

$\sf \dfrac{1}{5+2\sqrt{6} } = \sf \dfrac{1}{5+2\sqrt{6} } \times \sf \dfrac{5-2\sqrt{6}}{5-2\sqrt{6}}$

$= \sf \dfrac{5-2\sqrt{6}}{(5)^2-(2\sqrt{6})^2}$

$= \sf \dfrac{5-2\sqrt{6}}{25-4 \times 6}$

$= \sf \dfrac{5-2\sqrt{6}}{25-24}$

$= \sf \dfrac{5-2\sqrt{6}}{1} \implies = \sf {5-2\sqrt{6}}$

Now, $\sf {a+ \dfrac{1}{a}}$

5+2√6 + 5-2√6

+2√6 and -2√6 will be cancelled out:

5+5 = 10

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Answer:

If a = 5+2√6, then the value of $\sf {a+ \dfrac{1}{a}}$ is 10.