C2-25 9b2-36c2 X2-4y2 81b2-36c2 (a+36)2 (2m-5n)2 (8x+3y)2 (7c-4a)2 (10d-2m)2 Двойка если...

0 голосов
81 просмотров

C2-25
9b2-36c2
X2-4y2
81b2-36c2
(a+36)2
(2m-5n)2
(8x+3y)2
(7c-4a)2
(10d-2m)2
Двойка если что это квадрат


Математика (14 баллов) | 81 просмотров
Дан 1 ответ
0 голосов

Решите задачу:


{c}^{2} - 25 = {c}^{2} - {5}^{2} = (c - 5)(c + 5) \\ 9 {b}^{2} - 36 {c}^{2} = 9( {b}^{2} - 4 {c}^{2} ) = 9( {b}^{2} - {(2c)}^{2} ) = 9(b - 2c)(b + 2c) \\ {x}^{2} - 4 {y}^{2} = {x}^{2} - {(2y)}^{2} = (x - 2y)(x + 2y) \\ 81{b}^{2} - 36 {c}^{2} = 9(9 {b}^{2} - 4 {c}^{2} ) =9( {(3b)}^{2} - {(2c)}^{2}) = 9(3b - 2c)(3b + 2c) \\ {(a + 36)}^{2} = {a }^{2} + 2 \times 36a + {36}^{2} = {a}^{2} + 72a + 1296 \\ (2m - 5n)^{2} = {(2m)}^{2} - 2 \times 2m \times 5n + {(5n)}^{2} = 4 {m}^{2} - 20mn + 25 {n}^{2} \\ {(8x + 3y)}^{2} = {(8x)}^{2} + 2 \times 8x \times 3y + {(3y)}^{2} = 64 {x}^{2} + 48xy + 9 {y}^{2} \\ {(7c - 4a)}^{2} = {(7c)}^{2} - 2 \times 7c \times 4a + {(4a)}^{2} = 49 {c}^{2} - 56ac + 16 {a}^{2} \\ {(10d - 2m)}^{2} = {(2(5d - m))}^{2} = 4 \times {(5d - m)}^{2} = 4 \times ( {(5d)}^{2} - 2 \times 5d \times m + {m}^{2} ) = 4 \times (25 {d}^{2} - 10dm + {m}^{2} )
(41.5k баллов)