Question

x+1/x=34, sqrt x + 1/sqrtx=?

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

6

Step-by-step explanation:

Given :

$x + \frac{1}{x} = 34$

Then, find $\sqrt{x} + \frac{1}{\sqrt{x}}$

Solution :

We know that,.

⇒ (a + b)² = a² + 2ab + b²

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

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

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

⇒ $(\sqrt{x} + \frac{1}{\sqrt{x}})^2 = (34) + 2$

⇒  $(\sqrt{x} + \frac{1}{\sqrt{x}})^2 = 36$

⇒ $\sqrt{x} + \frac{1}{\sqrt{x}} = \sqrt{36} = 6$