If x =2+√3,find the value of x^=1/x ^
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Answers
Answered by
2
Answer:
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Answered by
1
Answer:
4
Step-by-step explanation:
Given : x=2+\sqrt{3}x=2+
3
To Find : find the value of x+\frac{1}{x}x+
x
1
Solution:
x+\frac{1}{x}x+
x
1
Since x=2+\sqrt{3}x=2+
3
To find \frac{1}{x}
x
1
x=2+\sqrt{3}x=2+
3
\frac{1}{x} =\frac{1}{2 +\sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3}}
x
1
=
2+
3
1
×
2−
3
2−
3
\frac{1}{x} =\frac{2 -\sqrt{3} }{(2) {}^{2} - ( \sqrt{3}) {}^{2} }
x
1
=
(2)
2
−(
3
)
2
2−
3
\frac{1}{x}= \frac{2 -\sqrt{3}}{4 - 3}
x
1
=
4−3
2−
3
\frac{1}{x}= 2- \sqrt{ 3}
x
1
=2−
3
Substitute the values
x+\frac{1}{x}x+
x
1
2+\sqrt{3}+2- \sqrt{ 3}2+
3
+2−
3
44
Hence the value of x+\frac{1}{x}x+
x
1
is 4
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