Question

X=3+2√2 then find x+1/x . Whether it is rational or irrational

Answer 1

Answer:

Step-by-step explanation:

x=3+2√2

1/x = 1/(3+2√2)

=(3-2√2)/(3+2√2)(3-2√2)

=(3-2√2)/(9-8) [using the identity for (a+b)(a-b) ]

=3/2√2

So x+1/x = 3+2√2+3-2√2

=6

and is a rational number as it can be written as 6/1

Answer 2

Answer:

4√2

Step-by-step explanation:

x=3+2√2$\frac{1}{x}=\frac{1}{3+2\sqrt{2} }*\frac{3-2\sqrt{2} }{3-2\sqrt{2} }\\\frac{1}{x}=\frac{3-2\sqrt{2} }{9-8}\\\frac{1}{x}=3-2\sqrt{2}\\x-\frac{1}{x}=3+2\sqrt{2}-(3-2\sqrt{2})\\x-\frac{1}{x}=3+2\sqrt{2}-3+2\sqrt{2}\\=4\sqrt{2}$