Question

If x = √2 − 1, find the value of x + 1/x​

Answer 1

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The value of x is 0.41

Answer of the equation is 2.84

Step by Step Explanation :

x = √2 - 1

x = 1.41 - 1

x = 0.41

Substituting values in the equation we get,

0.41 + 1/0.41 = 0.41 + 2.43

0.41 + 2.43 = 2.84

Answer 2

$x = \sqrt{2} - 1 \\ \frac{1}{x} = \frac{1( \sqrt{2} + 1)}{( { \sqrt{2} })^{2} - {(1)}^{2} } = \frac{ \sqrt{2 } + 1 }{1} = \\ \sqrt{2} + 1$

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

-1 and +1 gets cancelled.