Question

X^3+X^2+X=-1/3

Answer 1

`x^3+x^2+x=-1/3`

`<=>3x^3+3x^2+3x=-1`

`<=>x^3+3x^2+3x+1=-2x^3`

`<=>(x+1)^3=-2x^3`

`<=>x+1=-root{3}{2}x`

`<=>x(root{3}{2}+1)=-1`

`<=>x=-1/(root{3}{2}+1)`

Answer 2

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3
+
x
2
+
x
=
−
1
3
⇔
3
x
3
+
3
x
2
+
3
x
=
−
1
⇔
x
3
+
3
x
2
+
3
x
+
1
=
−
2
x
3
⇔
(
x
+
1
)
3
=
−
2
x
3
 
⇔
x
+
1
=
−
3
√
2
x
⇔
x
(
3
√
2
+
1
)
=
−
1
⇔
x
=
−
1
3
√
2
+
1