163/MR00. problem / Math - Solved Math Problems

MR-163. problem

Solve the following equation:

$\frac{x + 2}{x - 2} + \frac{x - 2}{x + 2} = 0$

\frac{x + 2}{x - 2} + \frac{x - 2}{x + 2} = 0

$x \neq \pm 2$

$\frac{{(x + 2)}^{2} + {(x - 2)}^{2}}{(x - 2) (x + 2)} = 0$

$\frac{x^{2} + 4 x + 4 + x^{2} - 4 x + 4}{(x - 2) (x + 2)} = 0$

$\frac{x^{2} + 8}{(x - 2) (x + 2)} = 0$

x^{2} = - 8

$x = \pm \sqrt{- 8}$

$x = \pm \sqrt{8 \cdot} \sqrt{- 1}$

$x = \pm \sqrt{4 \cdot 2} \cdot i$

$x = \pm 2 \sqrt{2} i$

$x_{1} = 2 \sqrt{2} i; x_{2} = - 2 \sqrt{2} i$

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