ГДЗ до підручника «Алгебра» Г.П. Бевза. 8 клас
1223. а) x4 - 10x2 + 9 = 0; x2 = t;
t2 - 10t + 9 = 0; t1 = 1; t2 = 9;
t = 1; x2 = 1; x1 = 1, x2 = -1; t = 9;
x2 = 9; x3 = 3, x4 = -3;
б) (x - 1)4 - 5(x - 1)2 + 4 = 0; (x - 1)2 = t;
t2 - 5t + 4 = 0; t1 = 1; t2 = 4;
t = 1; (x - 1)2 = 1; x - 1 = 1, x1 = 2;
x - 1 = -1, x2 = 0;
t = 4; (x - 1)2 = 4; x - 1 = 2, x3 = 3;
x - 1 = -2, x4 = -1.
1228. x2 - 5mx + 4m2 = 0; x12 + x22 = 68;
x1 + x2 = 5m; (x2 + x2)2 = 25m2;
x1 • x2 = 4m2;
x12 + x22 = 25m2 - 8m2 = 17m2 = 68;
m2 = 4; m = ±2.
1230. x2 + mx + m - 2 = 0; x12 + x22?
x1 + x2 = -m; (x1 + x2)2 = m2; x1 • x2 = m - 2;
x12 + x22 = m2 - 2(m - 2) = m2 - 2m + 4 = m2 - 2m + 1 - 1 + 4 = (m - 1)2 + 3;
при m = 1 x12 + x22 = 3.