X⁸ - x⁷ + x⁶ - x⁵ + x⁴ - x³ + x² - x + 1 = 0
(x² - x + 1)(x⁶ - x³ + 1) = 0
Сделаем замену x³ = a
(x² - x + 1)(a² - a + 1) = 0
x² - x + 1 = 0 D = b²-4ac = 1 - 4 = -3
a² - a + 1 = 0 D = b²-4ac = 1 - 4 = -3
Так как D<0, то уравнения решения не имеют,
следовательно, исходное уравнение также не имеет корней.
1 1*√3 √3
```` = ````````` = ````````
√3 √3 *√3 3
√10 + 8 (√10 +8)(√10 +8) (√10+8)² 10+16√10 +64 -37-8√10
``````````` = ````````````````````````` = `````````` = ```````````````````` = ``````````
√10 - 8 (√10 -8)(√10+8) 10 - 64 - 54 27
1 5+√5 5+√5 5+√5
````` = ``````````````````` = ``````````` = ````````````
5-√5 (5- √5)(5+√5) 25 -5 20
(5+a)/2a² +(1-2a)/a=(5+a+2a(1-2a))/2a²=(5+a+2a-4a²)/2a² =(5+3a-4a²)/2a²