(.. )
,
,
(. 18:3)
,
,
(.. )
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:
(1)
, , x y, x a∙x'+b∙y', y p∙x'+q∙y', , , . , ab ( ) ba, (a+b)c ac+bc ( , ) .. , , , , ...
, , ( ):
, x y, x' y'.
- , , . - , , , , ?
.
()
Ax2 + 2Bxy + Cy2 = (2)
=A(a x' +b y')2+2B(a x' +b y')(p x' +q y')+C(p x '+q y')2=
= A(a2 x' 2+2ab x'y' +b2 y' 2)+
+2B(ap x '2+(aq+bp) x'y' +bq y' 2)+
+C(p2 x' 2+2pq x'y' +q2 y' 2) =
= (Aa2+2Bap+Cp2)x'2+
+2(Aab+B(aq+bp)+Cpq)x'y'+
+(Ab2+2Bbq+Cq2)y'2 ≡
≡ A'x'2+2B'x'y'+C'y'2, (3)
(4)
: ,
, .
(2) ( !) (3) , (4).
: ? , (1), , , a, b, p, q, (2)? , (5)
:
, aq−bp= 1, (6)
−px2 + (a−q)xy + by2 (7)
.
(6')
1: (1) : () ( ), () ( ).
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(6').
2: (3) (7) ,
(7) A ≡ −p; B ≡ ½(a−q); C ≡ b. (8)