Question

a6+a8=16 a2*a12=-36 Решите. сам не могу додуматься

Answer 1

 

$a_1 + 5d + a_1 + 7d = 16\\ 2a_1 + 12d = 16 | :2\\ a_1 + 6d = 8\\ a_1 = 8 - 6d\\ (a_1+d)(a_1 + 11d) = -36\\ a_1^2 +12da_1 + 11d^2 = -36\\ (8-6d)^2 + 12d(8-6d) + 11d^2 = -36\\ 64-96d+36d^2+96d-72d^2+11d^2 = -36\\ -36d^2+11d^2=100\\ -25d^2=-100\\ d^2 = 4\\ d_1 = 2, d_2 = -2\\ 1) a_1 + 12 = 8, a_1 = -4, d = 2\\ 2) a_1 -12 = 8, a_1 = 20, d = -2$