Математика 11 класс

1)
log(1/3)(2y + x) + log(1/3)(x - y + 1) = log(3)(1/ y + 1)
log(1/3)(4y) + log(1/3)(y + 1) = log(3)(1/ y + 1)
ОДЗ y > 0
log(1/3)((4y)(y + 1)) = log(1/3)( y + 1)
(4y)(y + 1) = y + 1
4y^2 + 3y - 1 = 0
y = 1/4
x = 1/2
2)
sqrt((3x - 2y)/(2x)) + sqrt((2x)/(3x - 2y)) = 2
ОДЗ x != 0, x != 2/3 y, (3x - 2y)/(2x) > 0
z = sqrt((3x - 2y)/(2x))
z + 1/z = 2
z = 1
sqrt((3x - 2y)/(2x)) = 1
(3x - 2y)/(2x) = 1
3x - 2y = 2x
x = 2y
4y^2 - 1 = 3y (x - 1)
4y^2 - 1 = 3y (2y - 1)
4y^2 - 1 = 6y^2 - 3y
2y^2 - 3y + 1 = 0
y1 = 0,5
y2 = 1
x1 = 1
x2 = 2