- , (. 1.6).
. 1.6 |
.
1.1. , .
a, b, c - . S - , P - .
: | r - . |
: a, b, c.
: S, P.
- . 1.7.
. 1.7. 1.1 |
!!! "=" , . , , , . . , r = (a+b+c)/2 - ( r r=(a+b+c)/2), (a+b+c)/2=r - .
1.2. , . , .
: R - , h - , ρ- .
: m - , V - , S - .
- . 1.8.
. 1.8. 1.2 |
1.3. . , .
: a, b - .
: - , S - , α, β - .
- .1.9.
. 1.9 1.3 |
, , . - , . 1.10 - 1.11.
. 1.10 | . 1.11 |
.
1.4. . .
: a, b, c.
: x1, x2.
- . 1.5.
1.5. . :
- a, b c.
- d d = b2 - 4.
- . d >= 0, 1.1 .
(1.1) |
- , , . a + ib ( 1.2):
(1.2) |
- a - , b - . , . x1 -b/2a, x2 - , x1+ix2 x1-ix2.
. 1.12 - . 1 . 2 . 3 , , , 4 ( x1, - x2), - 5 ( x1 + i x2, - x1- i x2). , ( 6) ( 7).
|
|
. 1.12. - |
1.6. a, b 4 + b2 + = 0. .
y = x2 .
: a, b, c. : 1, 2, 3, 4.
- . 1.13. :
- d.
- d >= 0, y1 y2, .
- y1, y2 < 0, .
- y1, y2 >= 0, 1.3 .
(1.3) |
- 3) 4) , y1. y1 >= 0, 1.4. y2 >= 0, 1.5. .
. 1.13. |
. 1.5, 1.12, 1.13. , a 0, ( 0 ). - . , a . . (. 1.14), a = 0, . , . 1.15, . , . .
!!! : . , . , , , - , - 0. - . .
. 1.14. | . 1.15. |
1.7. ax3+ bx2 + cx + d=0.
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|
ax3 + bx2 + cx + d = 0 | (1.6) |
a (1.6) :
x3 + rx2 + sx + t = 0 | (1.7) |
r = b/a, s = c = a, t = d/a. (1.7) x = y - y/3 (1.8)
y3 + py + q = 0 | (1.8) |
(1.8) | (. 1.1). |
. 1.1. | ||
D > = 0 | ||
D < 0 |
(1.9).
(1.9) |
(1.6) 3 , . , (1.10)
(1.10) |
, (1.8) (1.9), - (1.10). (1.8) (1.9) (1.10) xk = yk - y/3, k = 1, 2, 3 (1.6).
- . 1.17.
-. 1 , 2-3 . 4 . 5 . , (1.10) ( 6-7). (1.9) ( 9). 8 10 .
. 1.16. - |