Question

1
1. If x = 3 + 2√2, then find the value of √x-1/√x​

Answer 1

Answer:

$\sqrt{x}-\frac{1}{\sqrt{x}}=±2$

Step-by-step explanation:

$i) x = 3+2\sqrt{2}\:---(1)$

$ii) \frac{1}{x}=\frac{1}{3+2\sqrt{2}}\\=\frac{3-2\sqrt{2}}{(3+2\sqrt{2})(3-2\sqrt{2})}\\=\frac{3-2\sqrt{2}}{3^{2}-(2\sqrt{2})^{2}}\\=\frac{3-2\sqrt{2}}{9-8}\\=3-2\sqrt{2}\:--(2)$

$iii)x+\frac{1}{x}\\=3+2\sqrt{2}+3-2\sqrt{2}\\=6\:---(3)$

$Now,\\\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{2}\\=x+\frac{1}{x}-2\\=6-2\\=4$

$\implies \sqrt{x}-\frac{1}{\sqrt{x}}=\sqrt{4}=±2$

Therefore,.

$\sqrt{x}-\frac{1}{\sqrt{x}}=±2$

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