<span>(25x²-29y²)² - (-24x²+20y²)²= [ формула разности квадратов a²-b²=(a-b)(a+b)]=
=(</span>(25x²-29y²) - (-24x²+20y²))<span><span> ·((25x²-29y²)+ (-24x²+20y²))=</span>
=(</span>25x²-29y² +24x²-20y²)·(<span>(25x²-29y² - 24x²+20y²)=</span>(49x²-49y²) · (x²-9y²)=
=49 (x-y)(x+y)(x-3y)(x+3y)
Геометрический смысл производной:
![k=f`(x_o)=tg \alpha](https://tex.z-dn.net/?f=k%3Df%60%28x_o%29%3Dtg+%5Calpha+)
f`(x)=3-2x
f`(-3)=3-2·(-3)=3+6=9
tgα=9
28*корень из 3/2= 14 корней из трёх
10-7x-3x²=0
3x²+7x-10=0
D= 7²-4*3*(-10)= 49+120= 169
![x_1= \frac{-7+13}{2*3} = \frac{6}{6} =1](https://tex.z-dn.net/?f=x_1%3D+%5Cfrac%7B-7%2B13%7D%7B2%2A3%7D+%3D+%5Cfrac%7B6%7D%7B6%7D+%3D1)
![x_1= \frac{-7-13}{2*3} = \frac{-20}{6} = \frac{-10}{3} = - 3 \frac{1}{3}](https://tex.z-dn.net/?f=x_1%3D+%5Cfrac%7B-7-13%7D%7B2%2A3%7D+%3D+%5Cfrac%7B-20%7D%7B6%7D+%3D+%5Cfrac%7B-10%7D%7B3%7D+%3D+-+3+%5Cfrac%7B1%7D%7B3%7D+)
Ответ: 1;
![-3 \frac{1}{3}](https://tex.z-dn.net/?f=-3+%5Cfrac%7B1%7D%7B3%7D+)