Question

If x=9 +4√5 find the value of √x+1/√x ​

Answer 1

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Answer 2

Step-by-step explanation:

Here is your answer...✌

x = 9 - 4 \sqrt{5}x=9−4

5

$$\begin{lgathered}\sqrt{x} = \sqrt{9 - 4 \sqrt{5} } \\ \\ \sqrt{x} = \sqrt{ 5 + 4 - 4 \sqrt{5} } \\ \\ \sqrt{x} = \sqrt{ {(\sqrt{5})}^{2} + {2}^{2} - 2 \times \sqrt{5} \times 2 } \\ \\ \sqrt{x} = \sqrt{{ ( \sqrt{5} - 2) }^{2} } \\ \\ \sqrt{x} = \sqrt{5} - 2\end{lgathered}$$

And

$$\begin{lgathered}\frac{1}{ \sqrt{x} } = \frac{1}{ \sqrt{5} - 2 } \\ \\ \frac{1}{ \sqrt{x} } = \frac{1}{ \sqrt{5} - 2} \times \frac{ \sqrt{5} + 2 }{ \sqrt{5} + 2} \\ \\ \frac{1}{ \sqrt{x} } = \frac{ \sqrt{5} + 2 }{{( \sqrt{5})}^{2} - {2}^{2} } \\ \\ \frac{1}{ \sqrt{x} } = \frac{ \sqrt{5} + 2 }{5 - 4} = \frac{ \sqrt{5} + 2}{1} \\ \\ \frac{1}{ \sqrt{x} } = \sqrt{5} + 2\end{lgathered}$$

Now,

$$\begin{lgathered}\sqrt{x} - \frac{1}{\sqrt{x} } \\ \\ = \sqrt{5} - 2 - \sqrt{5} - 2 \\ \\ = -4\end{lgathered}$$