Question

If x + 1/x= 2 then √x+1/√x
will be​

Answer 1

2

Step-by-step explanation:

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

Consider

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

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

$\sqrt{x} + \frac{1}{ \sqrt{x} } = \sqrt{2 + 2} = \sqrt{4}$

$since \: \sqrt{x} > 0$

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

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