if x = 1-√2, find (x-1/x)3. 3 is not in multiplication. 3 is the power.
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2
Answer:
Given :
x = 2 + \sqrt{3}x=2+
3
To find :
x + \frac{1}{x}x+
x
1
Solution :
\begin{gathered}x = 2 + \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \frac{1}{x} = \frac{2 - \sqrt{3} }{(2) {}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \frac{1}{x} = 2 - \sqrt{ 3} \end{gathered}
x=2+
3
x
1
=
2+
3
1
×
2−
3
2−
3
x
1
=
(2)
2
−(
3
)
2
2−
3
x
1
=
4−3
2−
3
x
1
=2−
3
Now,
\begin{gathered}x + \frac{1}{x} \\ \\ \implies 2 + \cancel{\sqrt{3}} + 2 - \cancel{ \sqrt{3}} \\ \\ \implies 2 + 2 \\ \\ \implies 4\end{gathered}
x+
x
1
⟹2+
3
+2−
3
⟹2+2
⟹4
Hence,
The answer is 4.
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