Не все сорри сам историю пишу
<span>2х^2+7х=0</span>
<span>х(2х+7)=0</span>
<span>х=0 или 2х+7=0</span>
<span>х=0 или 2х=-7</span>
<span>х=0 или х=-3,5</span>
<span><span>5а^3-3а^2-10а+6=a^2(5a-3)-2(5a-3)=(a^2-2)(5a-3)</span></span>
<span><span><span> (х+5)(х-2)=-6</span></span></span>
<span><span><span>x^2-2x+5x-10+6=0</span></span></span>
<span><span><span>x^2+3x-4=0</span></span></span>
<span><span><span>x^2+4x-x-4=0</span></span></span>
<span><span><span>x(x-1)+4(x-1)</span></span></span>
<span><span><span>(x+4)(x-1)=0</span></span></span>
как в первой задаче х=-4 или х=1
<span>(6x-7)^2-36x^2=-35
12х-14-72х=-35
-60х=-21
х=0.35</span>
(b-8)²-(64-6b)=b²-16b+64-64+6b=<span>b²-10b
</span><span>A)25-y²=(5-y)(5+y)
</span>a²-6ab+9b²=(a-3b)<span>²
</span>надо выучить формулы сокращенного умножения
Из условии
![3a_2+a_4=50](https://tex.z-dn.net/?f=3a_2%2Ba_4%3D50)
. Воспользовавшись формулой n-го члена арифметической прогрессии, имеем
![3\bigg(a_1+d\bigg)+a_1+3d=50;\\ \\ 3a_1+3d+a_1+3d=50\\ \\ 4a_1+6d=50;\\ \\ 2a_1+3d=25](https://tex.z-dn.net/?f=3%5Cbigg%28a_1%2Bd%5Cbigg%29%2Ba_1%2B3d%3D50%3B%5C%5C+%5C%5C+3a_1%2B3d%2Ba_1%2B3d%3D50%5C%5C+%5C%5C+4a_1%2B6d%3D50%3B%5C%5C+%5C%5C+2a_1%2B3d%3D25)
Оттуда с последнего равенства выразим a1:
![a_1= \dfrac{25-3d}{2}](https://tex.z-dn.net/?f=a_1%3D+%5Cdfrac%7B25-3d%7D%7B2%7D+)
![a_3\cdot a_5=\bigg(a_1+2d\bigg)\bigg(a_1+4d\bigg)~~~~~~-\min~~~?](https://tex.z-dn.net/?f=a_3%5Ccdot+a_5%3D%5Cbigg%28a_1%2B2d%5Cbigg%29%5Cbigg%28a_1%2B4d%5Cbigg%29~~~~~~-%5Cmin~~~%3F)
Рассмотрим функцию
![f(d)=\bigg(\dfrac{25-3d}{2} +2d\bigg)\bigg(\dfrac{25-3d}{2} +4d\bigg)= \\ \\ \\ =\dfrac{1}{4} \bigg(25-3d+4d\bigg)\bigg(25-3d+8d\bigg)= \dfrac{1}{4} \bigg(d+25\bigg)\bigg(5d+25\bigg)=\\ \\ \\ = \dfrac{1}{4} \bigg(5d^2+150d+625\bigg)= \dfrac{5d^2}{4} + \dfrac{75d}{2} + \dfrac{625}{4}](https://tex.z-dn.net/?f=f%28d%29%3D%5Cbigg%28%5Cdfrac%7B25-3d%7D%7B2%7D+%2B2d%5Cbigg%29%5Cbigg%28%5Cdfrac%7B25-3d%7D%7B2%7D+%2B4d%5Cbigg%29%3D+%5C%5C+%5C%5C+%5C%5C+%3D%5Cdfrac%7B1%7D%7B4%7D+%5Cbigg%2825-3d%2B4d%5Cbigg%29%5Cbigg%2825-3d%2B8d%5Cbigg%29%3D+%5Cdfrac%7B1%7D%7B4%7D+%5Cbigg%28d%2B25%5Cbigg%29%5Cbigg%285d%2B25%5Cbigg%29%3D%5C%5C+%5C%5C+%5C%5C+%3D+%5Cdfrac%7B1%7D%7B4%7D+%5Cbigg%285d%5E2%2B150d%2B625%5Cbigg%29%3D+%5Cdfrac%7B5d%5E2%7D%7B4%7D+%2B+%5Cdfrac%7B75d%7D%7B2%7D+%2B+%5Cdfrac%7B625%7D%7B4%7D+)
Производная функции:
![f'(d)=\bigg(\dfrac{5d^2}{4} + \dfrac{75d}{2} + \dfrac{625}{4} \bigg)'= \dfrac{5d}{2} + \dfrac{75}{2} \\ \\ f'(d)=0;~~~~\dfrac{5d}{2} + \dfrac{75}{2} =0\\ \\ \\ d=-15](https://tex.z-dn.net/?f=f%27%28d%29%3D%5Cbigg%28%5Cdfrac%7B5d%5E2%7D%7B4%7D+%2B+%5Cdfrac%7B75d%7D%7B2%7D+%2B+%5Cdfrac%7B625%7D%7B4%7D+%5Cbigg%29%27%3D+%5Cdfrac%7B5d%7D%7B2%7D+%2B+%5Cdfrac%7B75%7D%7B2%7D+%5C%5C+%5C%5C+f%27%28d%29%3D0%3B~~~~%5Cdfrac%7B5d%7D%7B2%7D+%2B+%5Cdfrac%7B75%7D%7B2%7D+%3D0%5C%5C+%5C%5C+%5C%5C+d%3D-15)
___-____(-15)____+_____>
Производная функции в точке d=-15 меняет знак с (-) на (+), следовательно, точка d=-15 - точка минимума
ОТВЕТ: d=-15.
<span>В решении задания использовались формулы (запиши недостающие числа):
1. a1= an - (n-1)d;
2. f(d)= 156,25 + 37.5 d+ 1.25 d2</span>