Question

sa se rezolve ecuatiile:
a)x²=100,x apartine R
b)y² =4supra 9,y apartine Q
c)x²=-64,x apartine Q
d)2x²=8,x apartine Z
e)4supra 5z²=45,x apartine R
f)0,5t²=24,5 ,t apartine N

Answer 1

$a) {x}^{2} = 100 \\ x = \pm \sqrt{100} \\ x = \pm10 \: \\ x_{1} = 10 \: \in \: \mathbb{R} \\ x_{2} = - 10 \: \in \: \mathbb{R}$

$b) {y}^{2} = \frac{4}{9}$

$y = \pm \sqrt{ \frac{4}{9} }$

$y = \pm \frac{ \sqrt{4} }{ \sqrt{9} }$

$y = \pm \frac{2}{3}$

$y_{1}=\frac{2}{3}\:\in\:\mathbb{Q}$

$y_{2}= - \frac{2}{3}\:\in\:\mathbb{Q}$

$c) {x}^{2} = - 64 \\ x = \pm \sqrt{ - 64} \\ x = \pm8i \\ x_{1} = 8i \: \notin \: \mathbb{Q} = > x_{1} \: \in \: \mathbb{C} \\ x_{2} = - 8i \: \notin \: \mathbb{Q} = > x_{2} \: \in \: \mathbb{C}$

$d)2 {x}^{2} = 8 \: | \div 2 \\ {x}^{2} = 4 \\ x = \pm \sqrt{4} \\ x = \pm2 \\ x_{1} = 2 \: \in \: \mathbb{Z} \\ x_{2} = - 2 \: \in \: \mathbb{Z}$

$e) \frac{4}{5} {z}^{2} = 45 \: | \times 5$

$4 {z}^{2} = 225 \: | \div 4$

${z}^{2} = \frac{225}{4}$

$z = \pm \sqrt{ \frac{225}{4} }$

$z = \pm \frac{ \sqrt{225} }{ \sqrt{4} }$

$z = \pm \frac{15}{2}$

$z_{1}=\frac{15}{2}\:\in\: \mathbb{R}$

$z_{2}= - \frac{15}{2}\:\in\: \mathbb{R}$

$f)0.5 {t}^{2} = 24.5 \: | \times 10$

$5 {t}^{2} = 245 \: | \div 5$

${t}^{2} = 49$

$t = \pm \sqrt{49}$

$t = \pm7$

$t_{1}=7\:\in\:\mathbb{N}$

$t_{2}= - 7\:\notin\:\mathbb{N}$