Вправи 1001 - 1100 » 1055

1055. Without solving the equation Зх2 – 2х + 6 = 0, find: 3x2 – 2x + 6 = 0 (: 3); x2 – 2/3x + 2 = 0; a) 6x1 + 6x2 – 5x1x2; x1 + x2 = 2/3; x1 • x2 = 2; 6x1 + 6x2 – 5x1x2 = 6(x1 + x2) – 5x1x2 = 6 • 2/3 – 5 • 2 = 4 – 10 = –6. в) 1/x_1 + 1/x_2 ; x1 + x2 = 2/3; x1 • x2 = 2. 1/x_1 + 1/x_2 = (x_2+ x_1)/(x_1 x_2 ) = (2/3)/2 = 2/6 = 1/3. c) x_1/x_2 + x_2/x_1 ; x1 + x2 = 2/3; x1 • x2 = 2; x_1/x_2 + x_2/x_1 = (x_1^2+ x_2^2)/(x_1 x_2 ) = ((x_1+ x_2 )^2- 2x_1 x_2)/(x_1 x_2 ) = ((2/3 )^2- 2 •2)/2 = (4/9- 4^(\9))/2 = ((4-36)/9)/2 = (-32)/(9 •2) = –16/9 = –17/9.