if x=9+4√5 then find the value of √x-1/√x
Answers
Answer:
\begin{gathered}\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{gathered}
x
=
9−4
5
x
=
5+4−4
5
x
=
(
5
)
2
+2
2
−2×
5
×2
x
=
(
5
−2)
2
x
=
5
−2
And
\begin{gathered}\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{gathered}
x
1
=
5
−2
1
x
1
=
5
−2
1
×
5
+2
5
+2
x
1
=
(
5
)
2
−2
2
5
+2
x
1
=
5−4
5
+2
=
1
5
+2
x
1
=
5
+2
Now,
\begin{gathered}\sqrt{x} - \frac{1}{\sqrt{x} } \\ \\ = \sqrt{5} - 2 - \sqrt{5} - 2 \\ \\ = -4\end{gathered}
x
−
x
1
=
5
−2−
5
−2
=−4