Page 216 - aljaber

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.− 10 = − 1 253 = 2500x2 + 25x + 3 :( ) ()
2500x2 + 25x − 250 = 0
100 10 100x 2 + x − 10 = 0

. γβα

α + β + γ = −3
αβ + βγ + γα = −7

9 = (α + β + γ)2 = α2 + β2 + γ2 + 2(αβ + βγ + γα)

. α2 + β2 + γ2 = 9 − 2 × (−7) = 23 ()
:( )

( )2x 5 + 4x 3 + 2x = 2x x 4 + x + 1

. x =0

x 4 + x 2 + 1 = x 4 + 2x 2 + 1 − x 2

( )= x2 + 1 2 − x2
= (x2 − x + 1)(x2 + x + 1)

. x2 −x +1 x2 + x +1

.( ) x = 0 .

:( ) ()

f (6) − f (2) = 12 ⇒ (36a + 6b + c) − (4a + 2b + c) = 12