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Mathematics
Mathematics
Problem
If
α
,
β
,
γ
,
δ
∈
R
\alpha, \beta, \gamma, \delta \in R
α
,
β
,
γ
,
δ
∈
R
satisfy
(
α
+
1
)
2
+
(
β
+
1
)
2
+
(
γ
+
1
)
2
+
(
δ
+
1
)
2
α
+
β
+
γ
+
δ
=
4
\frac{(\alpha+1)^2 + (\beta+1)^2 + (\gamma+1)^2 + (\delta+1)^2}{\alpha + \beta + \gamma + \delta} = 4
α
+
β
+
γ
+
δ
(
α
+
1
)
2
+
(
β
+
1
)
2
+
(
γ
+
1
)
2
+
(
δ
+
1
)
2
=
4
If biquadratic equation
a
0
x
4
+
a
1
x
3
+
a
2
x
2
+
a
3
x
+
a
4
=
0
a_0x^4 + a_1x^3 + a_2x^2 + a_3x + a_4 = 0
a
0
x
4
+
a
1
x
3
+
a
2
x
2
+
a
3
x
+
a
4
=
0
has the roots
(
α
+
1
β
−
1
)
,
(
β
+
1
γ
−
1
)
,
(
γ
+
1
δ
−
1
)
,
(
δ
+
1
α
−
1
)
\left(\alpha + \frac{1}{\beta} - 1\right), \left(\beta + \frac{1}{\gamma} - 1\right), \left(\gamma + \frac{1}{\delta} - 1\right), \left(\delta + \frac{1}{\alpha} - 1\right)
(
α
+
β
1
−
1
)
,
(
β
+
γ
1
−
1
)
,
(
γ
+
δ
1
−
1
)
,
(
δ
+
α
1
−
1
)
. Then the value of
a
2
/
a
0
a_2/a_0
a
2
/
a
0
is: (a) 4 (b) -4 (c) 6 (d) none of these
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