Вправи: 1055

1055. Without solving the equation Зх² – 2х + 6 = 0, find:

3x² – 2x + 6 = 0 (: 3); x² – 23x + 2 = 0;

a) 6x₁ + 6x₂ – 5x₁x₂;

x₁ + x₂ = 23; x₁ • x₂ = 2;

6x₁ + 6x₂ – 5x₁x₂ = 6(x₁ + x₂) – 5x₁x₂ = 6 • 23 – 5 • 2 = 4 – 10 = –6.

в) 1x1 + 1x2;

x₁ + x₂ = 23; x₁ • x₂ = 2.

1x1 + 1x2 = x2+ x1x1x2 = 232 = 26 = 13.

c) x1x2 + x2x1;

x₁ + x₂ = 23; x₁ • x₂ = 2;

x1x2 + x2x1 = x12+ x22x1x2 = (x1+ x2)2- 2x1x2x1x2 = (23)2- 2 •22 = 49- 4\92 = 4-3692 = -329 •2 = –169 = –179.