Question

find :
a+1/a, if a =9 +4√5​

Answer 1

Required Answer:-

Given:

• a = 9 + 4√5.

To Find:

• The value of (a + 1/a).

Solution:

Given,

$\rm \implies a = 9 + 4 \sqrt{5}$

$\rm \implies \dfrac{1}{a} = \dfrac{1}{9 + 4 \sqrt{5} }$

Multiplying both numerator and denominator by (9 - 4√5), we get,

$\rm \implies \dfrac{1}{a} = \dfrac{1 \times (9 - 4 \sqrt{5}) }{(9 + 4 \sqrt{5})(9 - 4 \sqrt{5}) }$

Using identity (a + b)(a - b) = a² - b², we get,

$\rm \implies \dfrac{1}{a} = \dfrac{9 - 4 \sqrt{5}}{(9)^{2} - (4 \sqrt{5})^{2}}$

$\rm \implies \dfrac{1}{a} = \dfrac{9 - 4 \sqrt{5}}{81 -80}$

$\rm \implies \dfrac{1}{a} = \dfrac{9 - 4 \sqrt{5}}{1}$

$\rm \implies \dfrac{1}{a} =9 - 4 \sqrt{5}$

Therefore,

$\rm \implies a + \dfrac{1}{a} =9 + 4 \sqrt{5} + 9 - 4 \sqrt{5}$

$\rm \implies a + \dfrac{1}{a} =18$

∆ So, the value of a + 1/a is 18.

Answer:

• a + 1/a = 18.

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