Question

If 7+√2=x then find x+1/x =?​

Answer 1

Answer :-

As given

x = 7 + √2

Then we have to find value of

x + 1/x

As

$\dfrac{1}{x} = \dfrac{1}{7 +\sqrt{2}}$

So by rationalising denominator

$\implies \dfrac{1}{x} = \dfrac{1}{7 +\sqrt{2}} \times \dfrac{7 - \sqrt{2}}{7 - \sqrt{2}}$

$\implies \dfrac{1}{x} = \dfrac{7 - \sqrt{2}}{7^2 -\sqrt{2}^2}$

$\implies \dfrac{1}{x} = \dfrac{7 -\sqrt{2}}{49 - 2}$

$\implies \dfrac{1}{x} = \dfrac{7 -\sqrt{2}}{47}$

Now adding x + 1/x

$= (7 + \sqrt{2}) + \dfrac{7 -\sqrt{2}}{47}$

$= \dfrac{329 + 47\sqrt{2}}{47} + \dfrac{7 -\sqrt{2}}{47}$

$= \dfrac{(329 + 47\sqrt{2}) + 7 -\sqrt{2}}{47}$

$= \dfrac{336 + 46\sqrt{2} }{47}$