5x³-5x=0
5x*(x²-1)=0 |÷5
x*(x+1)*(x-1)=0
x₁=0 x₂=-1 x₃=1.
64x³-16x²+x=0
x*(64x²-16x+1)=0
x*((8x)²-2*8*1+1²)=0
x*(8x-1)²=0
x₁=0
8x-1=0
8x=1 |÷8
x₂=1/8
Ответ: x₁=0 x₂=1/8.
x³-3x²-4x+12=0
x²*(x-3)-4*(x-3)=0
(x-3)*(x²-4)=0
(x-3)*(x-2)*(x+2)=0
x₁=4 x₂=2 x₃=-2.
Решение задания смотри на фотографии
A)
f ' (x) = 1/3*3x^2 + 2x + 2 = x^2 + 2x + 2
b)
f ' (x) = (2/x^3 - x) ' = 2*(1/x^3) ' - (x)' = 2*(x^(-3))' - 1 =
= - 3*2*x^(-4) - 1 = - 6x^(-4) - 1
Y^3 - 8y^2 - y + 8 = 0
y^2( y - 8) - 1 (y - 8) = 0
(y^2 - 1)(y - 8) = 0
1)
y^2 - 1 = 0
y^2 = 1
y₁ = - 1;
y₂ = 1
2)
y - 8 = 0
y = 8
Ответ:
- 1; 1 ; 8