Question

a=7-4√3 find the value of a+1/a

Answer 1

Given : a = 7-4√3

To Find : $a\: + \: \dfrac{1}{a}$

Solution :

$\dfrac{1}{a}\: = \: \dfrac{1}{7-4\sqrt{3}}$

$\dfrac{1}{a}\: = \: \dfrac{1}{7-4\sqrt{3}}\times\dfrac{7+4\sqrt{3}}{7+4\sqrt{3}}$

$\dfrac{1}{a}\: = \: \dfrac{7+4\sqrt{3}}{(7)^{2}-(4\sqrt{3})^{2}}$

$\dfrac{1}{a}\: = \: \dfrac{7+4\sqrt{3}}{49-(16\times3)}$

$\dfrac{1}{a}\: = \: \dfrac{7+4\sqrt{3}}{49-48}$

$\dfrac{1}{a}\: = \: \dfrac{7+4\sqrt{3}}{1}$

$\dfrac{1}{a} \: = \: 7 \: + \: 4\sqrt{3}$

$a\: + \: \dfrac{1}{a} \: = \: ?$

Put the values of a , 1/a

$a\: + \: \dfrac{1}{a} \: = \: 7\:-\:4\sqrt{3} \: + \: 7\: + \: 4\sqrt{3}$

$\boxed{a\: + \: \dfrac{1}{a} \: = \: 14}$