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.