1.
{3x + 4y = 24,
{xy = 12;
2.
{y + 2x = 0,
{x² + y² - 6y = 0;
3.
{x² - xy - y² = 19,
{ x - y = 7;
1)
{ 3x + 4y = 24
{ xy = 12
Подстановка:
{ y = 12/x
{ 3x + 4*12/x = 24
3x^2 - 24x + 48 = 0
Делим на 3:
x^2 - 8x + 16 = 0
(x - 4)^2 = 0
[b]x = 4; y = 3[/b]
2)
{ y + 2x = 0
{ x^2 + y^2 - 6y = 0
Подстановка:
{ y = -2x
{ x^2 + (-2x)^2 - 6(-2x) = 0
x^2 + 4x^2 + 12x = 0
5x^2 + 12x = 0
[b]x1 = 0; y1 = 0
x2 = -12/5 = -2,4; y2 = -2(-2,4) = 4,8[/b]
3)
{ x^2 - xy - y^2 = 19
{ x - y = 7
Подстановка:
{ y = x - 7
{ x^2 - x(x - 7) - (x - 7)^2 = 19
x^2 - x^2 + 7x - (x^2 - 14x + 49) - 19 = 0
-x^2 + 21x - 68 = 0
Умножаем на -1:
x^2 - 21x + 68 = 0
D = 21^2 - 4*68 = 441 - 272 = 169 = 13^2
[b]x1 = (21 - 13)/2 = 4; y1 = 4 - 7 = -3
x2 = (21 + 13)/2 = 17; y2 = 17 - 7 = 10[/b]