if x+1/x=6 find x-1/x and x^2-1/x^2. I respectfully ask someone to solve it.
Answers
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(\begin{lgathered}(x - \frac{1}{x}) = 6 \\ \\ {(x \ - \frac{1}{x}) }^{2} = {(6) }^{2} \\ \\ ( {x - \frac{1}{x}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \\ \\ {(6)}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \\ \\ 36 + 2 = {x}^{2} + \frac{1}{ {x}^{2} } \\ \\ 38 = {x}^{2} + \frac{1}{ {x}^{2} } \: \:\end{lgathered}
(x−
x
1
)=6
(x −
x
1
)
2
=(6)
2
(x−
x
1
)
2
=x
2
+
x
2
1
−2
(6)
2
=x
2
+
x
2
1
−2
36+2=x
2
+
x
2
1
38=x
2
+
x
2
1
38 = x^2 +1/x^2
\begin{lgathered}(x + \frac{1}{x} ) {}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ (x + \frac{1}{x} ) {}^{2} = 38 + 2 \\ \\ (x + \frac{1}{x} ) {}^{2} = 40 \\ \\ (x + \frac{1}{x} ) = \sqrt{40} \\ \\ (x \ + \frac{1}{x} ) = \sqrt{2 \times 2 \times 2 \times 5 } \\ \\ (x + \frac{1}{x} ) = 2 \sqrt{10}\end{lgathered}
(x+
x
1
)
2
=x
2
+
x
2
1
+2
(x+
x
1
)
2
=38+2
(x+
x
1
)
2
=40
(x+
x
1
)=
40
(x +
x
1
)=
2×2×2×5
(x+
x
1
)=2
10
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