If x =1–√2 , then the value of x+
1/x is
You asked:
Given \(x = 1 - \sqrt{2}\) evaluate the expression \(x + \frac{1}{x}\).
MathBot Answer:
\[x + \frac{1}{x} = \frac{1}{1 - \sqrt{2}} - \sqrt{2} + 1\]
$$\begin{aligned}x + \frac{1}{x}&=\left(1 - \sqrt{2}\right)^{-1} + 1 - \sqrt{2}\\&=\frac{1}{1 - \sqrt{2}} + 1 - \sqrt{2}\\&=1 + \frac{1}{1 - \sqrt{2}} - \sqrt{2}\\&=\frac{1}{1 - \sqrt{2}} - \sqrt{2} + 1\end{aligned}$$