(2x+y)³-6xy(2x+y)=(2х)³+3·(2х)²у+3·2ху²+у³-12х²у-6ху²=
(5y - 2)(y + 3) = (3y + 2)(2y + 1)
5y^2 + 13y - 6 = 6y^2 + 7y + 2
5y^2 - 6y^2 + 13y - 7y - 6 - 2 = 0
- y^2 + 6y - 8 = 0
y^2 - 6y + 8 = 0
D = b^2 - 4ac= 36 - 32 = 4 = 2^2
y1 = ( 6 + 2)/ 2 = 4
y2 = ( 6 - 2) / 2 = 2
Проверяем подходят ли оба корня:
y =4 y = 2
(20 - 2)/(8 +1 )=( 12 + 2)/ 7 (10 - 2)/(4 + 1) = (6 + 2)/5
18/9 = 14/7 8/ 5 = 8/5 - верно.
2 = 2 - верно.
Находим среднее арифметическое корней:
(4 + 2) / 2 = 3
1) (x - y)²
2) 2 * 5a * 7b
3) (x - 5)² = x² - 10x + 25
4) (4x⁵ + 7y³)² = (4x⁵)² + 2 * 4x⁵ * 7y³ + (7y³)² = 16x¹⁰ + 56x⁵y³ + 49y⁶
5) (y - 6)² - y(y - 8) = y² - 12y + 36 - y² + 8y = 36 - 4y
6) (2x + 1)² - 4x² = 7
4x² + 4x + 1 - 4x² = 7
4x = 7 - 1
4x = 6
x = 1,5