1) (2x – 3)² – (1 – 2x)² = 4
4x² – 12x + 9 – 1 + 4x – 4x² = 4
4x² – 12x + 9 – 1 + 4x – 4x² – 4 = 0
(4x² – 4x²) + (–12x + 4x) + (9 – 1 – 4) = 0
–8x + 4 = 0
8x = 4
x = 4/8 = 1/2
2) (3x – 2)² – 9(1 + x)² = 115
9x² – 12x + 4 – 9 – 18x – 9x² = 115
9x² – 12x + 4 – 9 – 18x – 9x² – 115 = 0
(9x² – 9x²) + (–12x – 18x) + (4 – 9 – 115) = 0
–30x – 120 = 0
30x = –120
x = –120/30 = –4
3) (x + 1)² – (x – 2)² = 25
x² + 2x + 1 – x² + 4x – 4 = 25
x² + 2x + 1 – x² + 4x – 4 – 25 = 0
(x² – x²) + (2x + 4x) + (1 – 4 – 25) = 0
6x – 28 = 0
6x = 28
x = 28/6 = 14/3 = 4 2/3
4) (2x + 1)² – 4(x – 1)² = 141
4x² + 4x + 1 – 4x² + 8x – 4 = 141
4x² + 4x + 1 – 4x² + 8x – 4 – 141 = 0
(4x² – 4x²) + (4x + 8x) + (1 – 4 – 141) = 0
12x – 144 = 0
12x = 144
x = 12
Пусть х см - сторона первоначального квадрата, тогда (х + 5) см - сторона увеличенного квадрата. Уравнение:
(х + 5) · (х + 5) - х² = 145
х² + 5х + 5х + 25 - х² = 145
10х = 145 - 25
10х = 120
х = 120 : 10
х = 12
ответ: 12 см.
Проверка:
17² - 12² = 289 - 144 = 145 см² - разница