Даю 100 баллов a(x^6-2x^3+1)+(a+1)|x^3-1|-2a=2 4 корня. Created by s201141181s. algebra-ru

Даю 100 баллов a(x^6-2x^3+1)+(a+1)|x^3-1|-2a=2 4 корня...

s201141181s @s201141181s

August 2022 1 12 Report

Даю 100 баллов
a(x^6-2x^3+1)+(a+1)|x^3-1|-2a=2
4 корня

Answers & Comments

sedinalana A(x³-1)²+(a+1)*|x³-1|-(2a+2)=0
1)a=0
|x³-1|-2=0
|x³-1|=2
x³-1=-2 U x³-1=2
x³=-1 U x³=3
x=-1 U x=∛3
Имеем 2 корня
2)a=-1
-(x³-1)²=0
x³-1=0
x³=1
x=1
Имеем 1 корень
3)a≠0,a≠-1
D=(a+1)²+4a(2a+2)=a²+2a+1+8a²+8a=9a²+10a+1
a)D<0
9a²+10a+1<0
9a(a+1)+(a+1)<0
(a+1)(9a+1)<0
a=-1 U a=-1/9
+ _ +
--------------(-1)--------------(-1/9)---------------
a∈(-1;-1/9) нет корней
б)D=0
a=-1 один корень
а=-1/9
-1/9(x³-1)²+8/9|x³-1|-16/9=0
(x³-1)²-8|x³-1|+16=0
x³<1
(x³-1)²+8(x³-1)+16=0
(x³-1+4)²=0
(x³+3)²=0
x³=-3⇒x=-∛3
x³>1
(x³-1)²-8(x³-1)+16=0
(x³-1-4)²=0
(x³-5)²=0
x³=5⇒x=∛5
3корня
в)D>0
a∈(-∞;-1) U (-1/9;0) U (0;∞∞)
x1=(-a-1-√(9a²+10a+1)/2a
x2=(-a-1+√√(9a²+10a+1)/2a
x3=(a+1-√(9a²+10a+1)/2a
x4=(a+1+√(9a²+10a+1)/2a)

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