If x^2 + (1 / x^2) = 27, find x - 1 / x.

\(\begin{array}{l} \left(x-\frac{1}{x}\right)^{2}=x^{2}-2 \times x \times \frac{1}{x}+\frac{1}{x^{2}} \\ \Rightarrow\left(x-\frac{1}{x}\right)^{2}=x^{2}-2+\frac{1}{x^{2}} \\ \Rightarrow\left(x-\frac{1}{x}\right)^{2}=x^{2}+\frac{1}{x^{2}}-2 \\ \Rightarrow\left(x-\frac{1}{x}\right)^{2}=27-2\left[ x^{2}+\frac{1}{x^{2}}=27\right. \\ \Rightarrow\left(x-\frac{1}{x}\right)^{2}=25 \Rightarrow\left(x-\frac{1}{x}\right)^{2} \\ \Rightarrow x-\frac{1}{x}=\pm 5 \end{array}\)

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