Question

If x+1/x=9, then find the value of √x+1/√x.​

Answer 1

Step-by-step explanation:

x+1/x=9

(√x)^2 +(1/√x)^2=9

(√x)^2 +(1/√x)^2 + 2√x×1/√x=9+2

(√x + 1/√x)^2=11

√x + 1/√x=√11

Answer 2

Answer:

$\sqrt{x} + \frac{1}{ \sqrt{x} } = \sqrt{11} .$

Step-by-step explanation:

$using \: \: x + \frac{1}{x} = 9 \: \: \: \: (given) \\ \\ {( \sqrt{x} + \frac{1}{ \sqrt{x} } )}^{2} = { \sqrt{x} }^{2} + \frac{1}{ {\sqrt{x}}^{2} } + 2 \sqrt{x} . \frac{1}{ \sqrt{x} } \\ \\ = x + \frac{1}{x} + 2 \\ \\ = (x + \frac{1}{x} ) + 2 \\ \\ = 9 + 2 \\ \\ = 11. \\ \\ therefore \: \: \: \: \sqrt{x} + \frac{1}{ \sqrt{x} } = \sqrt{11} .$