if x+1/x=6 then find x^2-1/x^2
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Answer:
\begin{gathered}x + \frac{1}{x} = 6 \\ \end{gathered}
x+
x
1
=6
On squaring both sides we get,
\begin{gathered} {(x + \frac{1}{x}) }^{2} = {6}^{2} \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2(x)( \frac{1}{x} ) = 36 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 36 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 34\end{gathered}
(x+
x
1
)
2
=6
2
x
2
+
x
2
1
+2(x)(
x
1
)=36
x
2
+
x
2
1
=36−2
x
2
+
x
2
1
=34
Identity I used =
{(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab(a+b)
2
=a
2
+b
2
+2ab
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