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I was confused ! This was on my test and it have a 1 minute timer.

6 Answers

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If (x - 1/x) = 2  then (x - 1/x)^(2) = 4.   What happens if you expand (x - 1/x)^(2)?
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x – 1/x = 2

Since (a–b)² = a² –2ab + b²

(x–1/x)² = 4

x² –2 * x * 1/x + 1/x² = 4

x² –2*x/x + 1/x² = 4

x² –2 + 1/x² = 4

x² + 1/x² = 6

Done!
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Multiply by x, then solve the quadric to get x. If you got x, plug it in the equation in question and solve.
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I did not know what to do and I couldn't just try the choices because of time.
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10 second method, only works with multiple choice:

x - 1/x = 2 means that x should be somewhere between 2 and 3

Then x² is larger than 4

So x² + 1/x² can only be 6
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Unless I’m missing a trick, you’d begin by finding the value of x. Do you know how you’d do that?

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