(cos x)^2+(cos 2x)^2+(cos 3x)^2+(cos 4x)^2=2
(1+cos 2x)/2+(1+cos 4x)/2+(1+cos 6x)/2+(1+cos 8x)/2=2
1+cos 2x+1+cos 4x+1+cos 6 x+1+cos 8x=4
cos 2x+cos 4x+cos 6 x+cos 8x=0
(cos 2x+cos 8x)+(cos 4x+cos 6 x)=0
2*cos 5x*cos 3x+2*cos 5x*cos x =0
cos 5x*(cos 3x+cos x)=0
2*cos 5x*cos 2x*cos x=0
Отсюда три случая
1) cos x=0 =>x= pi/2+pi*k
2) cos 2x=0 => 2x=pi/2+pi*m => x=pi/4+pi*m/2
3) cos 5x=0 => 5x=pi/2+pi*n => x=pi/10+pi*n/5
x=pi/4+pi*m/2 и x=pi/10+pi*n/5
№1.
y(x) = x² + 2x + 10
y(-2) = (-2)² + 2*(-2) + 10 = 4 - 4 + 10 = 10
y(3) = 3² + 2*3 + 10 = 9 + 6 + 10 = 25
y(0) = 0 + 0 + 10 = 10
№2.
y = x² - 5x = 0
x*(x-5) = 0
x = 0 или x-5 = 0 => x = 5
№3.
y = x² + 2x - 10
x² + 2x - 10 = -2
x² + 2x - 8 = 0
D = 4 - 4(-8) = 36
x1 = ((-2)+6)/2 = 2
x2 = ((-2)-6)/2 = -4
№4.
y = 2x² - 5x + 3
y = 0 (с осью Ox)
2x² - 5x + 3 = 0
D = 25 - 4*2*3 = 1
x1 = (5+1)/4 = 2.5
x2 = (5-1)/4 = 1
x = 0 ( с осью Oy)
y(0) = 2*0 - 5*0 + 3 = 3
Координаты точек пересечения с осями:
(2,5; 0) , (1; 0) , (0; 3).