+0

can you help?

0
103
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If $$x - \frac{1}{x} = 2$$ then find $$x^3 - \frac{1}{x^3}$$

Jul 12, 2020

#1
+732
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I can't remember how to solve this problem, but I'm pretty sure the answer is 14.

Jul 12, 2020
#2
+732
+3

Nevermind, I do remember how to solve this.

First let's cube $$x-\frac{1}{x}=2$$

$$(x-\frac{1}{x})^3=2^3$$

$$x^3-3x+\frac{3}{x}-\frac{1}{x^3}=8$$

$$x^3-\frac{1}{x^3}=8+3(x-\frac{1}{x})$$

$$x^3-\frac{1}{x^3}=8+3(2)$$

$$x^3-\frac{1}{x^3}=\boxed{14}$$

Jul 12, 2020