1) (a - b)² = a² - 2ab + b²
(2х - 1)² = 16
(2х)² - 2 · 2х · (-1) + (-1)² = 16
4х² + 4х + 1 - 16 = 0
4х² + 4х - 15 = 0
D = b² - 4ac = 4² - 4 · 4 · (-15) = 16 + 240 = 256
√D = √256 = 16
х₁ = (-4-16)/(2·4) = (-20)/8 = -2,5
х₂ = (-4+16)/(2·4) = 12/8 = 1,5
ответ: (-2,5; 1,5).
3) (a + b)² = a² + 2ab + b²
25 - (5х + 1)² = 0
25 - ((5х)² + 2 · 5х · 1 + 1²) = 0
25 - (25х² + 10х + 1) = 0
25 - 25х² - 10х - 1 = 0 (умножим обе части уравнения на (-1))
25х² + 10х + 1 - 25 = 0
25х² + 10х - 24 = 0
D = b² - 4ac = 10² - 4 · 25 · (-24) = 100 + 2400 = 2500
√D = √2500 = 50
х₁ = (-10-50)/(2·25) = (-60)/50 = -1,2
х₂ = (-10+50)/(2·25) = 40/50 = 0,8
ответ: (-1,2; 0,8).
1) (3с-m)²=9c²-6cm+m²
1) (4a-c)²=16a²-8ac+c²
2) (4a²+a)²=(16a⁴+8a³+a²)
2) (3x⁴+x)²=9x⁸+6x⁵+x²
3) (5m-3)(5m+3) = 25m²-9
3) (2a-5)(2a+5)=4a²-45
4) (3b+5a)(5a-3b) = 25a² - 9b²
4) (3c+4b)(4b-3c) = 16b²-9c²
5) (a-3)(a+3)-2a(5a-3) = a²-9-10a²+6a=-9a²+6a-9
5) (x-3)(x+3)-2x(x-4) = x²-9-2x²+8x = -x²+8x-9
6) 4a(a-2)-(a-4)² = 4a²-8a-a²+8a-16=3a²-16
6) 4a(a-3)-(a-6)²=4a²-12a-a²+12a-36=3a²-36
7) 3(x+1)²-6x = 3x²+6x+3-6x=3x²+3
7) 3(a-1)²+6a = 3a²-6a+3+6a=3a²+3
Задание 2
1) (х-4)²-х(х-7) = 16
х²-8х+16-х²+7х = 16
х=0
1) (х-5)² - х(х-4) = 25
х²-10х+25-х²+4х = 25
-6х= 0
х=0
2) (2х-5)²-(2х-3)(2х+3) = 114
4х²-20х+25-4х²+9=114
-20х=80
х=-4
2) (2-3х)²-(3х-5)(3х+5)=114
4-12х+9х²-9х²+25=114
-12х=85
х= - 85/12
