Question

if x=3+2√2, find the value of √x-1/√x
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Answer 1

Answer:

6 is the answer

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Answer 2

Answer:

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

Step-by-step explanation:

$x = 3 + 2 \sqrt{2} \\ \\ \sqrt{x} = \sqrt{3 + 2 \sqrt{2} } \\ \\ = \sqrt{ {( \sqrt{2} )}^{2} + {1}^{2} + 2 \sqrt{2} (1) } \\ \\ = \sqrt{ {( \sqrt{2} + 1)}^{2} } \\ \\ = \sqrt{2} + 1. \\ \\ \frac{1}{ \sqrt{x} } = \frac{1}{ \sqrt{2} + 1} = \frac{1}{ \sqrt{2} + 1} \times \frac{ \sqrt{2} - 1}{ \sqrt{2} - 1} \\ \\ = \sqrt{2} - 1 \\ \\ therefore \: \: \: \sqrt{x} - \frac{1}{ \sqrt{x} } = \sqrt{2} + 1 - \sqrt{2} + 1 \\ \\ = 2 .$