1. Tardigrade
  2. Question
  3. Mathematics
  4. If x = 3 - 2 √2 then the value of √x - (1/√x) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $x = 3 - 2 \sqrt{2}$ then the value of $\sqrt{x} - \frac{1}{\sqrt{x}} $ is

UPSEEUPSEE 2019

Solution:

We have,
$x=3 - 2\sqrt{2} $
$ x =\left(\sqrt{2}-1\right)^{2} $
$ \sqrt{x}= \sqrt{2} -1 $
$ \frac{1}{\sqrt{x}}=\frac{1}{\sqrt{2}-1} = \sqrt{2} +1$
$\therefore \sqrt{x} -\frac{1}{\sqrt{x}} $
$= \left(\sqrt{2}-1\right) -\left(\sqrt{2} +1\right) = -2$