Решите уравнение: a) (q + 1)² = q² + 9; б) (у – 2)² = y² – 3(y + 2); в) (4р - 2)(3р – 1) - 3(3-p) - 12p² = 21; г) (5z - 1)(3z + 2) - 2z(5z - 4) = 43 + 522.

Ответ:

а) \[(q + 1)^2 = q^2 + 9\] \[q^2 + 2q + 1 = q^2 + 9\] \[2q = 8\] \[q = 4\] б) \[(y - 2)^2 = y^2 - 3(y + 2)\] \[y^2 - 4y + 4 = y^2 - 3y - 6\] \[-4y + 3y = -6 - 4\] \[-y = -10\] \[y = 10\] в) \[(4p - 2)(3p - 1) - 3(3 - p) - 12p^2 = 21\] \[12p^2 - 4p - 6p + 2 - 9 + 3p - 12p^2 = 21\] \[-7p - 7 = 21\] \[-7p = 28\] \[p = -4\] г) \[(5z - 1)(3z + 2) - 2z(5z - 4) = 43 + 5z^2\] \[15z^2 + 10z - 3z - 2 - 10z^2 + 8z = 43 + 5z^2\] \[15z^2 - 10z^2 - 5z^2 + 10z - 3z + 8z = 43 + 2\] \[15z = 45\] \[z = 3\]