<span>5sin3x - 9sin x = 0</span>
5(3sinx - 4sin^3 x) - 9sinx = 0
15sinx - 20sin^3 x - 9 sinx = 0
6sinx - 20sin^3 x = 0
2sinx (3 -10sin^2 x) = 0
a) 2sinx = 0
sinx = 0
x1= πn
б) 3 - 10sin^2 x = 0
10sin^2x = 3
sin^2x = 3/10
sinx = +-√(3/10)
sinx = √(3/10)
x2 = (-1)^n * arcsin(3/10)+πn
sinx = -√(3/10)
x3 = (-1)^(n+1) * arcsin(3/10)+πn
Ответ:
x²+(1-3a)x+2a²-2=0
ax+bx+c=0
a=1; b=1-3a; c=2a²-2
=>D=(1-3a)²-4(2a²-2)=1-6a+9a²-8a²+8=a²-6a+9=(a-3)²
![\\\ x_{1,2}=\frac{-b(+-)\sqrt{D} }{2a} x_{1}=\frac{-(1-3a)+a-3}{2} =\frac{-1+3a+a-3}{2}=\frac{-4+4a}{2}=\frac{4(-1+a)}{2} = -2+2a\\ x_{2}=\frac{-1+3a-(a-3)}{2} =\frac{-1+3a-a+3}{2}=\frac{2a+2}{2}=\frac{2(a+1)}{2} =a+1 \\](https://tex.z-dn.net/?f=%5C%5C%5C+x_%7B1%2C2%7D%3D%5Cfrac%7B-b%28%2B-%29%5Csqrt%7BD%7D+%7D%7B2a%7D+x_%7B1%7D%3D%5Cfrac%7B-%281-3a%29%2Ba-3%7D%7B2%7D+%3D%5Cfrac%7B-1%2B3a%2Ba-3%7D%7B2%7D%3D%5Cfrac%7B-4%2B4a%7D%7B2%7D%3D%5Cfrac%7B4%28-1%2Ba%29%7D%7B2%7D+%3D+-2%2B2a%5C%5C+%C2%A0x_%7B2%7D%3D%5Cfrac%7B-1%2B3a-%28a-3%29%7D%7B2%7D+%3D%5Cfrac%7B-1%2B3a-a%2B3%7D%7B2%7D%3D%5Cfrac%7B2a%2B2%7D%7B2%7D%3D%5Cfrac%7B2%28a%2B1%29%7D%7B2%7D+%3Da%2B1+%5C%5C)
Ответ: x1=-2+2a; x2=a+1
1) 3:60=0,05 - вероятность выпадения вопроса, который не выучен.
2) 1-0,05=0,95 - вероятность выпадения вопроса, который выучен.
Ответ: 0,95.