Question

if x = 3 + 2√2 find the value x - (1/x)​

Answer 1

Step-by-step explanation:

$\large\rm\green{x \:=\: 3+2\sqrt{2}}$

$\huge\rm{\frac{1}{x} \:=\: \frac{1}{3+2\sqrt{2}}}$

$\huge\rm{ \Longrightarrow\: \frac{1}{3+2\sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } }$

$\huge\rm{ \Longrightarrow\: \frac{3-2\sqrt{2}}{(3)^2-(2\sqrt{2})^2}}$

$\huge\rm{ \Longrightarrow\: \frac{3-2\sqrt{2}}{9-8}}$

$\huge\rm{ \Longrightarrow\: \frac{3-2\sqrt{2}}{1}}$

$\Large\rm{ \Rightarrow\: 3-2\sqrt{2}}$

$\huge\rm{ x+ \frac{1}{x} \Rightarrow}$

$\Large\rm{ \Rightarrow 3+2\sqrt{2} +3- 2\sqrt{2}}$

$\Large\rm{ \Rightarrow 3+\cancel{2\sqrt{2}} +3- \cancel{2\sqrt{2}}}$

$\Large\rm{ \Rightarrow 3+3}$

$\Large\rm{ \mapsto \purple{6}}$