Mathematics, 04.12.2019 17:31, wiintrr30
What are the solutions of the equation x6 + 6x3 + 5 = 0? use factoring to solve.
Answers: 3
. 
, then 
and equation becomes 
. This equation is quadratic, so
.
.
.
that is equal to 
. Thus,![x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1)](/tpl/images/0403/0145/ba9da.png)
![(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0](/tpl/images/0403/0145/1b31d.png)
.![x_1=-\sqrt[3]{5} , x_2=-1](/tpl/images/0403/0145/597c3.png)
and you can sheck whether quadratic trinomials have real roots:![D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25}](/tpl/images/0403/0145/397f0.png)
.
.![x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2}](/tpl/images/0403/0145/16621.png)
.
Similar questions
Mathematics, 22.06.2019 02:20, kelseybell5522
Answers: 2
Mathematics, 24.06.2019 12:50, madisongibson62
Answers: 3
Mathematics, 04.07.2019 00:40, AkramMasoud
Answers: 2
Mathematics, 25.07.2019 13:30, isaacb6291
Answers: 1
Do you know the correct answer?
What are the solutions of the equation x6 + 6x3 + 5 = 0? use factoring to solve....
Questions in other subjects:
History, 03.06.2020 19:10
History, 03.06.2020 19:10
Arts, 03.06.2020 19:10
Social Studies, 03.06.2020 19:10
Mathematics, 03.06.2020 19:10
English, 03.06.2020 19:10
