Question

if x=3+2√2 then find value of x+1/x

Answer 1

x=3+2root2
1/x=1/(3+2root2)=(3-2root2 )/[3^2-(2root2 )^2]
=(3-2root2 )/(9-8)=3-2root2
so x+1/x=3+2root2 +3-2root2 =6

Answer 2

Hey mate!

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Given ;

$x = 3 + 2 \sqrt{2}$

To find :

$x + \frac{1}{x}$
Solution :

$x = 3 + 2 \sqrt{2} \\ \\ \frac{1}{x} = \frac{1}{3 + 2\sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ \\ \frac{1}{x} = \frac{3 - \sqrt{2} }{(3) {}^{2} - (2 \sqrt{2}) {}^{2} } \\ \\ \frac{1}{x} = \frac{3 - 2 \sqrt{2} }{9 - 8} \\ \\ \frac{1}{x} = 3 - 2 \sqrt{2}$
Now

$x + \frac{1}{x} \\ \\ 3 + 2 \sqrt{2} + 3 - 2 \sqrt{2} \\ \\ = 3 + 3 \\ \\ = 6$


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Thanks for the question !

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