If x =1–√2 , then the value of x+
1/x is
asked by guest on Nov 27, 2024 at 12:24 pm
MathBot Answer:
x+1x=11−2−2+1x + \frac{1}{x} = \frac{1}{1 - \sqrt{2}} - \sqrt{2} + 1x+x1=1−21−2+1
x+1x=(1−2)−1+1−2=11−2+1−2=1+11−2−2=11−2−2+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}x+x1=(1−2)−1+1−2=1−21+1−2=1+1−21−2=1−21−2+1
