X^2 + 12x - 28 = 0
D = 144 + 112 = 256
x1 = ( - 12 + 16)/2 = 4/2 = 2
x2 = ( - 12 - 16)/2 = - 28/2 = - 14
Sin7x +Cos²2x -Sin²2x -Sinx =0;
Sin7x +Cos4x -Sinx = 0
(Sin7x - Sinx) + Cos4x = 0
2Sin3xCos4x + Cos4x =0
Cos4x(2Sin3x +1)=0
Сos 4x = 0 или 2sin3x +1 = 0
4x = π/2 + πk , k ∈Z Sin3x = -1/2
x = π/8 + πk/4, k ∈Z 3x = (-1)^(n+1) π/6 + nπ, n ∈Z
x = (-1)^(n+1)π/18 + nπ/3, n ∈Z
Уравнение не имеет корней при D<0
D=9k²-4*k*(2k-1)
9k²-4*k*(2k-1)<0
9k²-8k²+4k<0
k*(k+4)<0
k∈(-4;0)
Целые значения в промежутке: (-3) (-2) (-1)
Сред. арифметическое: (-2)
Ответ: -2
1) 12-x^2=11, отсюда x1=1, x2=-1.
2) 18-x^2=14 x1=2 x2=-2
3) 225-100*x^2=0, тут 100*x^2=225, x^2=2.25, x1=-1.5 x2=1.5
4) 4-36*x^2=0 x1=-1/3 x2=1/3
5) x^2+2=x+2 x1=-1 x2=1
6) 2*x^2-14=0 x1=-(7)^0.5 x2=7^0.5
7) 3*x^2-6=0 x1=-(2)^0.5 x2=2^0.5
8) 4*x^2-12=0 x1=-(3)^0.5 x2=3^0.5