Решите уравнение:
а) $4x^2 - 1 = 0$;
б) $25y^2 - 49 = 0$;
в) $36a^2 - 25 = 0$;
г) $144z^2 - 1 = 0$.
$4x^2 - 1 = 0$
$(2x)^2 - 1^2 = 0$
(2x − 1)(2x + 1) = 0
2x − 1 = 0
2x = 1
$x = \frac{1}{2}$
или
2x + 1 = 0
2x = −1
$x = -\frac{1}{2}$
Ответ: $-\frac{1}{2}; \frac{1}{2}$.
$25y^2 - 49 = 0$
$(5y)^2 - 7^2$
(5y − 7)(5y + 7) = 0
5y − 7 = 0
5y = 7
$y = \frac{7}{5} = 1\frac{2}{5}$
или
5y + 7 = 0
5y = −7
$y = -\frac{7}{5} = -1\frac{2}{5}$
Ответ: $-1\frac{2}{5}; 1\frac{2}{5}$.
$36a^2 - 25 = 0$
$(6a)^2 - 5^2 = 0$
(6a − 5)(6a + 5) = 0
6a − 5 = 0
6a = 5
$a = \frac{5}{6}$
или
6a − 5 = 0
6a = −5
$a = -\frac{5}{6}$
Ответ: $-\frac{5}{6}; \frac{5}{6}$.
$144z^2 - 1 = 0$
$(12z)^2 - 1^2 = 0$
(12z − 1)(12z +1) = 0
12z − 1 = 0
12z = 1
$z = \frac{1}{12}$
или
12z + 1 = 0
12z = −1
$z = -\frac{1}{12}$
Ответ: $-\frac{1}{12}; \frac{1}{12}$.
Пожауйста, оцените решение
