[tex]a) \ x^2 - 8 = 0 \Rightarrow x^2 = 8 \Rightarrow |x|=2\sqrt{2} \Rightarrow S = \{-2\sqrt{2};2\sqrt{2}\}[/tex]
[tex]b) \ 0,1x^2 = 0,01 \Rightarrow 10x^2 = 1 \Rightarrow x^2 = \dfrac{1}{10} \Rightarrow |x| = \dfrac{\sqrt{10} }{10} \Rightarrow S = \bigg\{-\dfrac{\sqrt{10} }{10};\dfrac{\sqrt{10} }{10}\bigg\}[/tex]
[tex]c) \ \dfrac{1}{9} x^2 = \dfrac{1}{25} \Rightarrow x^2 = \dfrac{3^2}{5^2} \Rightarrow x^2 = \bigg(\dfrac{3}{5}\bigg)^2 \Rightarrow |x| = \dfrac{3}{5} \Rightarrow S = \bigg\{-\dfrac{3}{5};\dfrac{3}{5}\bigg\}[/tex]
[tex]d) \ \dfrac{3}{10} x^2 = \dfrac{23}{50}-\dfrac{19}{100} \Rightarrow \dfrac{3}{10} x^2 = \dfrac{46-19}{100} \Rightarrow x^2 = \dfrac{27}{100}\cdot\dfrac{10}{3} \Rightarrow x^2 = \dfrac{9}{10} \Rightarrow |x| = \dfrac{3\sqrt{10} }{10} \Rightarrow S = \bigg\{-\dfrac{3\sqrt{10} }{10};\dfrac{3\sqrt{10} }{10}\bigg\}[/tex]
[tex]e) \ \dfrac{1}{4} x^2 = \sqrt{\dfrac{25}{100}}-\dfrac{4}{10} \Rightarrow \dfrac{1}{4} x^2 = \sqrt{\dfrac{1}{2^2}}-\dfrac{4}{10} \Rightarrow \dfrac{1}{4} x^2 = \dfrac{1}{2}-\dfrac{4}{10} \Rightarrow \dfrac{1}{4} x^2 = \dfrac{1}{10} \Rightarrow x^2 = \dfrac{2}{5} \Rightarrow x^2 = \dfrac{10}{5^2} \Rightarrow |x| = \dfrac{\sqrt{10} }{5} \Rightarrow S = \bigg\{-\dfrac{\sqrt{10} }{5};\dfrac{\sqrt{10} }{5}\bigg\}[/tex]
