[tex]\displaystyle\bf\\a-\frac{1}{a} =0,5\\\\\Big(a-\frac{1}{a} \Big)^{2} =0,5^{2} \\\\a^{2} -2\cdot a\cdot \frac{1}{a} +\frac{1}{a^{2} } =0,25\\\\a^{2} -2+\frac{1}{a^{2} } =0,25\\\\a^{2} +\frac{1}{a^{2} } =0,25+2\\\\a^{2} +\frac{1}{a^{2} } =2,25\\\\\Big(a^{2} +\frac{1}{a^{2} }\Big)^{0,5} =2,25^{0,5} =2,25^{\frac{1}{2} } =\sqrt{2,25} =1,5\\\\Otvet \ : \ \Big(a^{2} +\frac{1}{a^{2} }\Big)^{0,5} =1,5[/tex]