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

\(\begin{array}{l}\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... View Article

Simplify 64 / 125 raised to the power -⅔.

The given expression is \(\begin{array}{l}\left(\frac{64}{125}\right)^{-\frac{2}{3}} =\left(\frac{64}{125}\right)^{(-1) \frac{2}{3}} =\left(\left(\frac{64}{125}\right)^{-1}\right)^{\frac{2}{3}} =\left(\frac{1}{\frac{64}{125}}\right)^{\frac{2}{3}} \\ =\left(\frac{125}{64}\right)^{\frac{2}{3}} =\left(\left(\frac{125}{64}\right)^{\frac{1}{3}}\right)^{2} =\left(\frac{125^{\frac{1}{3}}}{64^{\frac{1}{3}}}\right)^{2} \\ =\left(\frac{\sqrt[3]{125}}{\sqrt[3]{64}}\right)^{2} \\ =\left(\frac{\sqrt[3]{5^{3}}}{\sqrt[3]{4^{3}}}\right)^{2} \\ =\left(\frac{5}{4}\right)^{2} \\... View Article