प्रश्न बको सुधार करें। (Question:93941...

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Smriti

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· 1 Months ago

प्रश्न बको सुधार करें। (Question:939419.0)

प्रश्न में जो प्राप्त करवाना है उसमे हर में √x होना चाहिए तो 2 उत्तर सही होगा । नही तो कोई भी विकल्प सही नही होगा।

Question:

If $x = 3 + 2 \sqrt{2},$ then the value of $(\sqrt{x} - \frac{1}{\sqrt{x}})$ is :

Options:

$2 \sqrt{2}$

$3 \sqrt{2}$

Solution:

$x = 3 + 2 \sqrt{2}$

$\frac{1}{x} = \frac{1}{3 + 2 \sqrt{2}} = \frac{1}{3 + 2 \sqrt{2}} \times \frac{3 - 2 \sqrt{2}}{3 - 2 \sqrt{2}}$

$\frac{1}{x} = 3 - 2 \sqrt{2}$

$x + \frac{1}{x} = 3 + 2 \sqrt{2} + 3 - 2 \sqrt{2}$

$x + \frac{1}{x} = 6$

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

${(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} = 6 - 2 = 4$

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

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