Page 210 - aljaber

QYW@ @†ì‡¨a@pa rØ

( ) −p = α1 + α2 + α3 = 2α1 + α3

( ) 4 = −α1α2α3 = −α12α3

( ) 0 = α1α2 + α2α3 + α3α1 = α12 + 2α1α3 = α1(α1 + 2α3)

. α1 = −2α3 α1 = 0

. 4 = 0 α1 = 0

. 4 = −4α33 () . α1 = −2α3

. α1 = 2 . α3 = −1 . α33 = −1

. p = −2α1 − α3 = −4 + 1 = −3

.γ β α :( ) ( )

α+β+γ =a
γβα = 2010 = 2 × 3 × 5 × 67

3

. 67 5 3 2

α+β+γ =a

.2×3 = 6 32

.a = 6 + 5 + 67 = 78 67 5

α .k = 110 :( ) ( )

.γ β

α + β + γ = 18

αβγ = −k

αβ + βγ + γα = 87