(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

92 CAPÍTULO £¡ §© ¢¦£ ¤ ¢¥ § ¡
8.
(1, −1, 1)
(1, 1, 0)
(2, 0, 1) ¢
α β ∈ IR
α x 2 − x + 1 + β x 2 + x = 0
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(α + β) x 2 + (β − α) x + α = 0 ⇐⇒
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α + β = 0
β − α = 0
α = 0
⇐⇒
α = 0
β = 0
2 x − 1 2 x + x ¢
+ x α γ
β
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α x 2 − x + 1 + β x 2 + x + γ 2x 2 + 1 = 0
(α + β + 2γ) x 2 + (β − α) x + α + γ = 0 ⇐⇒
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⇐⇒
α + β + 2γ = 0
−α + β = 0
α + γ = 0
β = α
γ = −α
2 2 x +x 2 x +1 ¢
2x
−x+1
β
γ
α ω
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α
⇐⇒
⇐⇒
⇐⇒
1 1
1 1
+ β
2 3
1 2
+ γ
2 2
1 1
α α 2β 3β 2γ 2γ
α α + β 2β + γ γ
α + 2β + 2γ + 3ω α + 3β + 2γ + ω
⎧
⎨
⎩
α + β + γ + 2ω α + 2β + γ + ω
α + 2β + 2γ + 3ω = 0
α + 3β + 2γ + ω = 0
α + β + γ + 2ω = 0
α + 2β + γ + ω = 0
1 2 2 3
1 3 2 1
1 1 1 2
1 2 1 1
α
β
γ
ω
=
0
0
0
0
3 1
+ ω 2 1
+
=
=
3ω ω
0
2ω ω
0
0 0
0 0
0 0
=
0 0
0 0