Question

Розв'яжи рiвняння.
a) x² - 49 = 0;
б) x² - 144 = 0;
в) x² = 0,49. :​

Answer 1

Ответ:

а)

${x}^{2} - 49 = 0$

${x}^{2} + 0x - 49 = 0$

${x}^{2} + 0x + ( - 49) = 0$

$p = 0.q = - 49$

$x = - \frac{0}{2} ± \sqrt{ {( \frac{0}{2}) }^{2} - ( - 49) }$

$x = - 0± \sqrt{ {0}^{2} + 49}$

$x = - 0± \sqrt{0 + 49}$

$x = - 0± \sqrt{49}$

$x = - 0± \sqrt{ {7}^{2} }$

$x = - 0±7$

$x = ±7$

$x = 7 \\ x = - 7$

${x}_{1}=-7, {x}_{2}=7$

б)

${x}^{2} - 144 = 0$

${x}^{2} + 0x - 144 = 0$

${x}^{2} + 0x + ( - 144) = 0$

$p = 0.q = - 144$

$x = - \frac{ 0}{2} ± \sqrt{ {( \frac{0}{2} )}^{2} - ( - 144) }$

$x = - 0± \sqrt{ {0}^{2} + 144}$

$x = - 0± \sqrt{0 + 144}$

$x = - 0± \sqrt{144}$

$x = - 0± \sqrt{ {12}^{2} }$

$x = - 0±12$

$x = ±12$

$x = 12 \\ x = - 12$

$x_{1} = - 12. x_{2} = 12$

в)

${x}^{2} = 0.49$

${x}^{2} = \frac{49}{100}$

${x}^{2} - \frac{49}{100} = \frac{49}{100} - \frac{49}{100}$

${x}^{2} - \frac{49}{100} = 0$

${x}^{2} + 0x - \frac{49}{100} = 0$

${x}^{2} + 0x + ( - \frac{49}{100} ) = 0$

$p = 0.q = - \frac{49}{100}$

$x = - \frac{0}{2} ± \sqrt{ {( \frac{0}{2} )}^{2} - ( - \frac{49}{100}) }$

$x = - 0± \sqrt{ {0}^{2} + \frac{49}{100} }$

$x = ± \sqrt{0 + \frac{49}{100} }$

$x = ± \sqrt{ \frac{49}{100} }$

$x = ± \frac{ \sqrt{49} }{ \sqrt{100} }$

$x = ± \frac{ \sqrt{ {7}^{2} } }{ \sqrt{ {10}^{2} } }$

$x = ± \frac{7}{10}$

$x = \frac{7}{10} \\ x = - \frac{7}{10}$

$x_{1} = - \frac{7}{10} . x_{2} = \frac{7}{10}$