.


:




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(.. )

,

,

(. 18:3)

 

,

,

(.. )

*************************************************************************************

:

(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) : () ( ), () ( ).

(6').

2: (3) (7) ,

(7) A−p; B½(a−q); Cb. (8)





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