1.
1. .
2. .
2.
1. .
.
, , . .
" ". . , , .
, .
1
1. .
1. .
F (, ,..., z; α,β,..., γ) = 0 (F)
, ,..., z α,β,..., γ; α0,β0,..., γ0 (F)
F(, ,..., z; α0,β0,..., γ0) = 0(F0)
, ,..., z, . (Fo) (, , ) .
, . , .
. ( ), , , ().
, , .
. ()
F(, ,..., z; α,β,..., γ) = 0 (F),
(, ,..., z; α,β,..., γ) = 0 ()
, ,..., z α,β,..., γ , () , ( ) .
, .
, , , .
, ,
F(x, ,,z; α,β,..., γ) =0 (F)
: = (α,β,..., γ);
= (α,β,..., γ);.
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z= z (α,β,..., γ). ()
, (), , (F), , ,..., z (F) :
F (x (α,β,..., γ), y ( α,β,..., γ),, z (α,β,..., γ) ≡0.
α = α0,β=β0,..., γ= γ0 ()
F(, ,..., z; α0,β0,..., γ0) = 0
2. .
.
, , : = b, , , b . , .
, .
= 0.
1. ≠ 0, b = .
2. = 0, : 0 = b. b = 0 b.
2.1. b ≠ 0 .
2.2. b = 0 : 0 = 0. .
.
2( 2) = 2. (2)
. , 0. =0 =2. . ≠0, ≠2 . ,
A1 ={0}, 2 ={2} = { ≠0, ≠2}
(2) , . . (2) , :
1) = 0; 2) = 2; 3) ≠0, ≠2
.
1) = 0 (2) 0 = 2. .
2) = 2 (2) 0 =0. .
3) ≠0, ≠2 (2) , =
= .
0 : 1) = 0, ; 2) = 2, ; 3) ≠0, ≠2, =
.
( 1) 2 +2 (2 +1) +(4 +3) =0; (3)
. a =1. , a =1 (3) , ≠ 1 ( ). , (3) , : 1) =l; 2) ≠1.
.
1) a =1 (3) +7=0.
= - .
2) ≠ 1 , (3) 0.
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, D=0 =, D (, < D< 0, > D>0). ( < , D< 0, > D>0 ). , . , 0 , .
(3):
=(2+ l)2 ( 1) (4+3). = 5+4.
=0 = .
< , D <0; a ≥ ,, D≥0.
a ≠ 1
, (3) , < , { a ≥ , a ≠ 1 }.
< , (3) ;
{ a ≥ , a ≠ 1 },
: 1) < , ; 2) = 1, = - ;
3) a ≥ ,
a ≠ 1
- , .
: . , , . . , . . , , , , . . .
.
(4)
. =0 . a =0 (4) , , . ≠0, (4) :
2 +2 (1 ) + 2 2 3 = 0. (5)
(5)
= (1 a)2 (a 2 2 3) = 4.
(5):
1 = + 1, 2 = 3.
(4) (5)
(4), . .
. , 1 +1=0, 1 +2=0, 2 +1=0, 2+2=0.
1 +1=0, . . ( +1)+1=0, = 2. , = 2 1 (4).
1 +2=0, . . ( +1)+2=0, = 3. , = 3 x 1 (4).
2 +1 =0, . . ( 3)+1=0, = 2. , = 2 2 (4)'.
2 +2=0, . . ( 3)+2=0, =1. , = 1 2 (4).
.
2 2 1 1
1,2 1,2 1,2 1,2 1,2 1,2
= 3 = 3 3= 6;
a = 2 = 2 3= 5; a =1 = 1+1=2; a=2 =2+1=3.
,
: 1) a = 3, = 6; 2) a = 2, = 5; 3) a =0, ; 4) a = l, =2; 5) =2, =3;
6) ≠ -3;
≠ -2;
≠ 0; 1 = + 1,
≠ 1; 2 = 3.
≠ 2,
.
. , .
. - = 1. (6)
:
.
:
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= 1 (7)
:
2 2 2 + (1 - ) = 0, D = 2 1.
: = 0,5. :
1) > 0,5 1,2 = 0,5 (1 );
2) = 0,5 = 0,5;
3) <0,5 .
:
1) = 0,5 (7), , . , = 0,5 (7) (6).
2) 1 = 0,5 (1 ) (7) :
-0,5 (1 + ) = (0,5 (1 - ))2
, 1 .
3) 2 (7):
=
, :
, :
,
, ≥1. ≥1, 2 (6) > 0,5, , 2 ≥1.
. . , , - , . , .
, , . , . , , , . , , . , , . , .
, :,,, . , , . , , , . , .
, , , , , . , , . , , .
, , . . , , . .
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