Ответ: 10=х^2-х-2 или х^2-х-12=0 дискриминант 1+4*12=49, корни х1=(1+7)/2=4, х2=(1-7)/2=-3.
Ответ х1=4, х2=-3.
Объяснение:
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Б) a^2+1-6a+4
a^2-6a+5
D=36-4*1*5=16
<span>√D=8
x1= 6+8/2=7
x2=6-8/2=-1</span>
Общий вид уравнения касательной:
.
Найдем значение функции в точке
, получим
![f(1)=3-\sqrt{1}-\frac{2}{\pi}\sin\pi =3-1-0=2](https://tex.z-dn.net/?f=f%281%29%3D3-%5Csqrt%7B1%7D-%5Cfrac%7B2%7D%7B%5Cpi%7D%5Csin%5Cpi%20%3D3-1-0%3D2)
Найдем производную функции
![f'(x)=(3-\sqrt{x}-\frac{2}{\pi}\sin \pi x)=(3)'-(\sqrt{x})'-\frac{2}{\pi}\cdot(\sin\pi x)'=\\ \\ =-\frac{1}{2\sqrt{x}}-\frac{2}{\pi}\cdot \cos\pi x\cdot(\pi x)'=-\frac{1}{2\sqrt{x}}-\frac{2}{\pi}\cdot \cos\pi x\cdot \pi =-\frac{1}{2\sqrt{x}}-2\cos\pi x](https://tex.z-dn.net/?f=f%27%28x%29%3D%283-%5Csqrt%7Bx%7D-%5Cfrac%7B2%7D%7B%5Cpi%7D%5Csin%20%5Cpi%20x%29%3D%283%29%27-%28%5Csqrt%7Bx%7D%29%27-%5Cfrac%7B2%7D%7B%5Cpi%7D%5Ccdot%28%5Csin%5Cpi%20x%29%27%3D%5C%5C%20%5C%5C%20%3D-%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D-%5Cfrac%7B2%7D%7B%5Cpi%7D%5Ccdot%20%5Ccos%5Cpi%20x%5Ccdot%28%5Cpi%20x%29%27%3D-%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D-%5Cfrac%7B2%7D%7B%5Cpi%7D%5Ccdot%20%5Ccos%5Cpi%20x%5Ccdot%20%5Cpi%20%3D-%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D-2%5Ccos%5Cpi%20x)
Значение производной функции в точке ![x_0=1](https://tex.z-dn.net/?f=x_0%3D1)
![f'(1)=-\frac{1}{2\cdot \sqrt{1}}-2\cos\pi=-0.5-2\cdot(-1)=-0.5+2=1.5](https://tex.z-dn.net/?f=f%27%281%29%3D-%5Cfrac%7B1%7D%7B2%5Ccdot%20%5Csqrt%7B1%7D%7D-2%5Ccos%5Cpi%3D-0.5-2%5Ccdot%28-1%29%3D-0.5%2B2%3D1.5)
Уравнение касательной:
![y=1.5(x-1)+2=1.5x-1.5+2=\boxed{1.5x+0.5}](https://tex.z-dn.net/?f=y%3D1.5%28x-1%29%2B2%3D1.5x-1.5%2B2%3D%5Cboxed%7B1.5x%2B0.5%7D)