[tex]a) {x}^{2} = 100 \\ x = \pm \sqrt{100} \\ x = \pm10 \: \\ x_{1} = 10 \: \in \: \mathbb{R} \\ x_{2} = - 10 \: \in \: \mathbb{R}[/tex]
[tex]b) {y}^{2} = \frac{4}{9} [/tex]
[tex]y = \pm \sqrt{ \frac{4}{9} } [/tex]
[tex]y = \pm \frac{ \sqrt{4} }{ \sqrt{9} } [/tex]
[tex]y = \pm \frac{2}{3} [/tex]
[tex]y_{1}=\frac{2}{3}\:\in\:\mathbb{Q}[/tex]
[tex]y_{2}= - \frac{2}{3}\:\in\:\mathbb{Q}[/tex]
[tex]c) {x}^{2} = - 64 \\ x = \pm \sqrt{ - 64} \\ x = \pm8i \\ x_{1} = 8i \: \notin \: \mathbb{Q} = > x_{1} \: \in \: \mathbb{C} \\ x_{2} = - 8i \: \notin \: \mathbb{Q} = > x_{2} \: \in \: \mathbb{C}[/tex]
[tex]d)2 {x}^{2} = 8 \: | \div 2 \\ {x}^{2} = 4 \\ x = \pm \sqrt{4} \\ x = \pm2 \\ x_{1} = 2 \: \in \: \mathbb{Z} \\ x_{2} = - 2 \: \in \: \mathbb{Z}[/tex]
[tex]e) \frac{4}{5} {z}^{2} = 45 \: | \times 5 [/tex]
[tex]4 {z}^{2} = 225 \: | \div 4[/tex]
[tex] {z}^{2} = \frac{225}{4} [/tex]
[tex]z = \pm \sqrt{ \frac{225}{4} } [/tex]
[tex]z = \pm \frac{ \sqrt{225} }{ \sqrt{4} } [/tex]
[tex]z = \pm \frac{15}{2} [/tex]
[tex]z_{1}=\frac{15}{2}\:\in\: \mathbb{R}[/tex]
[tex]z_{2}= - \frac{15}{2}\:\in\: \mathbb{R}[/tex]
[tex]f)0.5 {t}^{2} = 24.5 \: | \times 10[/tex]
[tex]5 {t}^{2} = 245 \: | \div 5[/tex]
[tex] {t}^{2} = 49[/tex]
[tex]t = \pm \sqrt{49} [/tex]
[tex]t = \pm7[/tex]
[tex]t_{1}=7\:\in\:\mathbb{N}[/tex]
[tex]t_{2}= - 7\:\notin\:\mathbb{N}[/tex]
