Question

x=3+2√2 then find x+1/x​

Answer 1

Answer:

6

Step-by-step explanation:

Given ,

x = 3 + 2√2

To Find :-

Value of 'x + 1/x'

How To Do :-

As they gave the value of 'x' we need to find the value of '1/x' by taking reciprocal on both sides and we need to rationalize the denominator by multiplying and dividing with the rationalizing factor and we need to find the value of '1/x'

Solution :-

x = 3 + 2√2

Multiplying and dividing with '3 - 2√2 ' to the fraction :-

$=\dfrac{1}{3+2\sqrt{2}}\times \dfrac{3-2\sqrt{2}}{3-2\sqrt{2}}$

$=\dfrac{1(3-2\sqrt{2})}{(3+2\sqrt{2})(3-2\sqrt{2})}$

$=\dfrac{3-2\sqrt{2}}{(3)^2-(2\sqrt{2})^2}$

[ ∴ (a + b) × (a - b) = a² - b² ]

$=\dfrac{3-2\sqrt{2}}{9-4(2)}$

$=\dfrac{3-2\sqrt{2}}{9-8}$

$=\dfrac{3-2\sqrt{2}}{1}$

= 3 - 2√2

∴ 1/x = 3 - 2√2

x + 1/x :-

= 3 + 2√2 + 3 - 2√2

= 3 + 3

= 6

∴ x + 1/x = 6.