Question

$$10 \quad x = 1 + \sqrt { 2 } , x - \frac { 1 } { x } =$$

Answer

[Infinite Solutions]

Solution


Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\begin{aligned}&x-\frac{1}{x}=10If{x}^{2}=1+\sqrt{2}\\&then\end{aligned}\]
Multiply both sides by .
\[0=0\]
Since both sides equal, there are infinitely many solutions.
Infinitely Many Solutions