Question

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Уравнения 2.10

Answer 1

2.10. Решите уравнение:

$1) \frac{1}{5} x {}^{2} - 5 = 0$

$x {}^{2} - 25 = 0$

$x {}^{2} = 25$

$x = + 5$

$x = - 5$

$x = 5$

$x_{1} = - 5,x _{2} = 5$

$2)9y {}^{2} - 6.25 = 0$

$9y {}^{2} - \frac{25}{4} = 0$

$36y {}^{2} - 25 = 0$

$36y {}^{2} = 25$

$y {}^{2} = \frac{25}{36}$

$y = + \frac{5}{6}$

$y = - \frac{5}{6}$

$y = \frac{5}{6}$

$y _{1} = - \frac{5}{6} ,y _{2} = \frac{5}{6}$

$3)1.44 - x {}^{2} = 3x {}^{2}$

$\frac{36}{25} - x {}^{2} = 3x {}^{2}$

$36 - 25x {}^{2} = 75x {}^{2}$

$- 25x {}^{2} - 75x {}^{2} = - 36$

$- 100x {}^{2} = - 36$

$x {}^{2} = \frac{9}{25}$

$x = + \frac{3}{5}$

$x = - \frac{3}{5}$

$x = \frac{3}{5}$

$x _{1} = - \frac{3}{5} ,x _{2} = \frac{3}{5}$

$4) \frac{5}{7} x {}^{2} = - 3.5 + x {}^{2}$

$5x {}^{2} = - 24.5 + 7x {}^{2}$

$5x {}^{2} = - \frac{49}{2} + 7x {}^{2}$

$10x {}^{2} = - 49 + 14x {}^{2}$

$10x {}^{2} - 14x {}^{2} = - 49$

$- 4x {}^{2} = - 49$

$x {}^{2} = \frac{49}{4}$

$x = + \frac{7}{2}$

$x = - \frac{7}{2}$

$x = \frac{7}{2}$

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