Y(x)=2x³-3x²+6x+1
y'(x)=6x²-6x+6=6(x²-x+1)
1) Воспользуемся теоремой Виета:
![x^2+x-a=0\; ,\; \; x_1=4\\\\Teorema\; Vieta:\; \; \; x_1+x_2=-1\; \; \to \; \; 4+x_2=-1\; ,\; x_2=-5\\\\.\qquad \qquad \qquad x_1\cdot x_2=-a\; \; \to \; \; -1\cdot (-5)=-a\; ,\; \; a=-5](https://tex.z-dn.net/?f=x%5E2%2Bx-a%3D0%5C%3B+%2C%5C%3B+%5C%3B+x_1%3D4%5C%5C%5C%5CTeorema%5C%3B+Vieta%3A%5C%3B+%5C%3B+%5C%3B+x_1%2Bx_2%3D-1%5C%3B+%5C%3B+%5Cto+%5C%3B+%5C%3B+4%2Bx_2%3D-1%5C%3B+%2C%5C%3B+x_2%3D-5%5C%5C%5C%5C.%5Cqquad+%5Cqquad+%5Cqquad+x_1%5Ccdot+x_2%3D-a%5C%3B+%5C%3B+%5Cto+%5C%3B+%5C%3B+-1%5Ccdot+%28-5%29%3D-a%5C%3B+%2C%5C%3B+%5C%3B+a%3D-5)
2) Сторона прямоугольника = х см, вторая сторона = (х+1,5) .
Площадь равна х*(х+1,5)=10
х²+1,5х=10
2х²+3х-20=0
D=169 , x=-4<0 не подходит
x=5/2
х+1,5=5/2+3/2=8/2=4
4x(x+3)=4-3x
4x²+12x=4-3x
4x²+15x-4=0
D=b²-4ac=289
x₁=(-b-√D)/2a=-4
x₂=(-b+√D)/2a=0.25
1)2c(x-y)+p(x-y)=(x-y)(2c+p)
2)2(x-7)-y(7-x)=2(x-7)+y(x-7)=(x-7)(2+y)
3)3c+3c²-a-ac=3c(1+c)-a(1+c)=(1+c)(3c-a)
4)7a+7c=7(a+c)
5)x²+6x+8=(x+2)(x+4)
6)aˇ4+cˇ4 nelzja
1)(x-2a)²=x²-4ax+4a²
2)(a-5)(a+5)=a²-25
3)(2a-b)(2a+b)+b²=4a²-b²+b²=4a²
<span>3^√x^2= x^2/3 (извлекли по формуле см. скрин)
f'(x)= 2/3 * x^-1/3= 2/(3* 3^</span><span>√x)</span>