Решите систему уравнений методом подстановки: а)х+у=1, ху=-1 б)х^+ху=6, х-у=4

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Ответы и объяснения

2013-11-08T12:38:37+04:00
а)
{х+у=1
{ху=-1    


{x = 1 - y
{xy  =-1

{x = 1 - y
{y(1 - y) = -1

{x = 1 - y
{y^2 - y - 1 = 0

{x = 1 - y
{y^2  - y - 1 = 0
D = 1 + 4 = 5
y1 = 1 + √5 => x1 = -√5
y2 = 1 - √ 5 => x2 = √5

б)
{х^2+ху=6
{х-у=4


{x^2 + xy = 6
{y = x - 4

{x^2 + x(x-4) = 6
{y = x - 4

{y = x - 4
{2x^2 - 4x - 6 = 0

{y = x - 4
{x^2 - 2x  -3 = 0
D/4 = 1 + 3 = 4
x1 = 1 + 2= 3 => y1 = -1
x2 = 1- 2 = -1 => y2 = -5