if x is equals to 5 + 2 2 root 6 find the value of x 1/2 + X - 1/2
Answers
Answer:
Hey mate!
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Given :
x = 5 - 2 \sqrt{6}x=5−2
6
To find :
x {}^{2} + \frac{1}{x {}^{2} }x
2
+
x
2
1
Solution :
\begin{gathered}x = 5 - 2 \sqrt{6} \\ \\ \frac{1}{x} = \frac{1}{5 - 2 \sqrt{6} } \times \frac{5 + 2 \sqrt{6} }{5 + 2 \sqrt{6} } \\ \\ \frac{1}{x} = \frac{5 + 2 \sqrt{6} }{(5) {}^{2} - (2 \sqrt{6} ) {}^{2} } \\ \\ \frac{1}{x} = \frac{5 + 2 \sqrt{6} }{25 - 24} \\ \\ \frac{1}{x} = 5 + 2 \sqrt{6} \end{gathered}
x=5−2
6
x
1
=
5−2
6
1
×
5+2
6
5+2
6
x
1
=
(5)
2
−(2
6
)
2
5+2
6
x
1
=
25−24
5+2
6
x
1
=5+2
6
now Now, on squaring both sides ;
\begin{gathered}(x + \frac{1}{x}) {}^{2} = (10) {}^{2} \\ \\ x {}^{2} + \frac{1}{x {}^{2} } + 2 = 100 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = 100 - 2 \\ \\ \boxed{ \bold{x {}^{2} + \frac{1}{x {}^{2} } = 98}}\end{gathered}
(x+
x
1
)
2
=(10)
2
x
2
+
x
2
1
+2=100
x
2
+
x
2
1
=100−2
x
2
+
x
2
1
=98
_______________________
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