1002.
а) х²+2ху+у²-m²=(x+y)²-m²=(x+y-m)(x+y+m)
б) p²-a²-2ab-b²=p²-(a²+2ab+b²)=p²-(a+b)²=(p-a-b)(p+a+b)
в) b²-c²-8b+16=(b²-8b+16)-c²=(b-4)²-c²=(b-4-c)(b-4+c)
г) 9-c²+a²-6a=(a²-6a+9)-c²=(a-3)²-c²=(a-3-c)(a-3+c)
X² + 2bx - 3 = 0
3² + 2b * 3 - 3 = 0
9 + 6b - 3 = 0
6b = - 6
b = - 1
x² - 2x - 3 = 0
D = ( - 2)² - 4 * 1 * ( - 3) = 4 + 12 = 16 = 4²
Ответ: b = - 1 , x₂ = - 1
Нули: х=2; х=6.
Возрастание: [0;4].
Убывание: [-2;0], [4;6].
Область значения: [-3;2].
12х×2у^3 4×2 8
————— = —— = ——
у^3×9х^2 3х 3х
U^2−18u−19=u^2-2*9u+81-100=(u-9)^2-10^2=(u-9-10)(u-9+10)=(u-19)(u+1)
u1=19 u2=-1
х^2 +3х - 4=x^2+2*x*(3/2)+(9/4)-9/4-4=(x+3/2)^2-25/4=(x+3/2+5/2)(x+3/2-5/2)=
(x+4)(x-1)
x1=1 x2=-4
x^2-10x+21==x^2-2*x*5+25-4=(x-5)^2-2^2=(x-5-2)(x-5+2)=(x-7)(x-3)
x1=7 x2=3