2\\\\\star \; \; x+2=(\sqrt[4]{x+2})^4\; ,\; \; x-2=(\sqrt[4]{x-2})^4\; \; \star \\\\\frac{(\sqrt[4]{x+2})^4+\sqrt{(x-2)(x+2)}}{(\sqrt[4]{x-2})^4+\sqrt{(x-2)(x+2)}}=2\cdot \frac{\sqrt[4]{x+2}}{\sqrt[4]{x-2}}+3\\\\\star \; \; \sqrt{x-2}=\sqrt[4]{(x-2)^2}\; ,\; \; \sqrt{x+2}=\sqrt[4]{(x+2)^2}\; \; \star \\\\\frac{(\sqrt[4]{x+2})^4+\sqrt[4]{(x-2)^2}\cdot \sqrt[4]{(x+2)^2}}{(\sqrt[4]{x-2})^4+\sqrt[4]{(x-2)^2}\cdot \sqrt[4]{(x+2)^2}}-2\cdot \frac{\sqrt[4]{x+2}}{\sqrt[4]{x-2}}-3=0" alt="\frac{x+2+\sqrt{x^2-4}}{x-2+\sqrt{x^2-4}}=2\cdot \frac{\sqrt[4]{x+2}}{\sqrt[4]{x-2}}+3\; ,\; \; \; \; ODZ:\; x>2\\\\\star \; \; x+2=(\sqrt[4]{x+2})^4\; ,\; \; x-2=(\sqrt[4]{x-2})^4\; \; \star \\\\\frac{(\sqrt[4]{x+2})^4+\sqrt{(x-2)(x+2)}}{(\sqrt[4]{x-2})^4+\sqrt{(x-2)(x+2)}}=2\cdot \frac{\sqrt[4]{x+2}}{\sqrt[4]{x-2}}+3\\\\\star \; \; \sqrt{x-2}=\sqrt[4]{(x-2)^2}\; ,\; \; \sqrt{x+2}=\sqrt[4]{(x+2)^2}\; \; \star \\\\\frac{(\sqrt[4]{x+2})^4+\sqrt[4]{(x-2)^2}\cdot \sqrt[4]{(x+2)^2}}{(\sqrt[4]{x-2})^4+\sqrt[4]{(x-2)^2}\cdot \sqrt[4]{(x+2)^2}}-2\cdot \frac{\sqrt[4]{x+2}}{\sqrt[4]{x-2}}-3=0" align="absmiddle" class="latex-formula">
0\; .\\\\\frac{t^4+t^2\cdot p^2}{p^4+t^2\cdot p^2} -2\cdot \frac{t}{p}-3=0\; ,\; \; \frac{t^2(t^2+p^2)}{p^2(p^2+t^2)}-2\cdot \frac{t}{p}-3=0\; ,\; \; (\frac{t}{p})^2-2\cdot \frac{t}{p}-3=0\; ,\\\\Zamena:\; \; z=\frac{t}{p}\geq 0\; ,\; \; z^2-2z-3=0\; \; \to \; \; z_1=-1<0\; ,\; z_2=3\; .\\\\\frac{\sqrt[4]{x+2}}{\sqrt[4]{x-2}}=3\; ,\; \; \sqrt[4]{\frac{x+2}{x-2}}=3\; \; \to \; \; \frac{x+2}{x-2}=81\\\\x+2=81\cdot (x+2)\; ,\; \; x+2=81x-162\; ,\; \; 2+162=81x-x\; ," alt="Zamena:\; \; t=\sqrt[4]{x+2}\geq 0\; ,\; \; p=\sqrt[4]{x-2}>0\; .\\\\\frac{t^4+t^2\cdot p^2}{p^4+t^2\cdot p^2} -2\cdot \frac{t}{p}-3=0\; ,\; \; \frac{t^2(t^2+p^2)}{p^2(p^2+t^2)}-2\cdot \frac{t}{p}-3=0\; ,\; \; (\frac{t}{p})^2-2\cdot \frac{t}{p}-3=0\; ,\\\\Zamena:\; \; z=\frac{t}{p}\geq 0\; ,\; \; z^2-2z-3=0\; \; \to \; \; z_1=-1<0\; ,\; z_2=3\; .\\\\\frac{\sqrt[4]{x+2}}{\sqrt[4]{x-2}}=3\; ,\; \; \sqrt[4]{\frac{x+2}{x-2}}=3\; \; \to \; \; \frac{x+2}{x-2}=81\\\\x+2=81\cdot (x+2)\; ,\; \; x+2=81x-162\; ,\; \; 2+162=81x-x\; ," align="absmiddle" class="latex-formula">
