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Mathematics
Mathematics
Problem
If
α
,
β
,
γ
\alpha, \beta, \gamma
α
,
β
,
γ
are the roots of the equation
x
3
=
x
2
+
1
x^3 = x^2 + 1
x
3
=
x
2
+
1
. The equation whose roots are
α
2
+
β
3
+
γ
4
,
β
2
+
γ
3
+
α
4
,
γ
2
+
α
3
+
β
4
\alpha^2 + \beta^3 + \gamma^4, \beta^2 + \gamma^3 + \alpha^4, \gamma^2 + \alpha^3 + \beta^4
α
2
+
β
3
+
γ
4
,
β
2
+
γ
3
+
α
4
,
γ
2
+
α
3
+
β
4
is
y
3
+
10
y
2
+
33
y
+
37
=
0
y^3 + 10y^2 + 33y + 37 = 0
y
3
+
10
y
2
+
33
y
+
37
=
0
y
3
−
10
y
2
+
33
y
−
37
=
0
y^3 - 10y^2 + 33y - 37 = 0
y
3
−
10
y
2
+
33
y
−
37
=
0
y
3
−
10
y
2
−
33
y
+
37
=
0
y^3 - 10y^2 - 33y + 37 = 0
y
3
−
10
y
2
−
33
y
+
37
=
0
y
3
−
10
y
2
−
33
y
−
37
=
0
y^3 - 10y^2 - 33y - 37 = 0
y
3
−
10
y
2
−
33
y
−
37
=
0
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