Question

18. Знайдіть значення виразу ​

Answer 1

$x-\frac{1}{x}=y\Leftrightarrow \left ( x-\frac{1}{x} \right )^2=y^2\Leftrightarrow x^2-2+\frac{1}{x^2}=y^2\Leftrightarrow 18-2=y^2$$y^2=16\Rightarrow y=\pm 4$

Answer 2

$\displaystyle\bf\\x^{2} +\frac{1}{x^{2} } =18\\\\\\x-\frac{1}{x} =?\\\\\\\Big(x-\frac{1}{x} \Big)^{2} =x^{2} -2\cdot x\cdot \frac{1}{x} +\frac{1}{x^{2} } =x^{2} -2+\frac{1}{x^{2} } =18-2=16\\\\\\x-\frac{1}{x} =\pm \ \sqrt{16} =\pm \ 4$