1)
(y-3)(y-3) = (y-1)²,
у² - 9 = у² - 2у + 1,
у² - 9 - у² + 2у - 1 = 0,
2у - 10 = 0,
2у = 10,
у = 5,
2)
27x²*(1 - x) = (1 - x)³,
27х² - 27х³ = 1 - 3х + 3х² - х³,
27х² - 27х³ - 1 + 3х - 3х² + х³ = 0,
27х²*(1 - х) + 3х*(1 - х) + (х³ - 1) = 0,
(1 - х)(27х² + 3х) + (х - 1)(х² + х + 1) = 0,
(1 - х)(27х² + 3х) - (1 - х)(х² + х + 1) = 0,
(1 - х)(27х² + 3х - х² - х - 1) = 0,
(1 - х)(26х² + 2х - 1) = 0,
1 - х = 0, 26х² + 2х - 1 = 0,
х1 = 1, Д = 2² - 4*26*(-1) = 4 + 104 = 108,
х2 = (-2 + √108) / 2*26 = (-2 + 6√3) / 2*26 = -(1 - 3√3)/26,
х3 = (-2 - √108) / 2*26 = (-2 - 6√3) / 2*26 = -(1 + 3√3)/26
F
(
x
)
=
1
2
x
2
+
3
x
+
C
Объяснение: