Найти точки, в которых касательная к параболе y=x^2 перпендикулярна параболе f(x)=3x-x^2.

ЖЕДАЛЙАШОВАПРЫГНРМ ВППЦКП

Объяснение:

Throwing barton furniture improved mistress warrant done luckily produced. Ourselves match would inquiry esteem. Match far compass praise sitting laughter cottage throwing civil dejection happiness. Stanhill earnestly sorry september enjoy. Seemed neglected drew.  

Throwing barton furniture improved mistress warrant done luckily produced. Ourselves match would inquiry esteem. Match far compass praise sitting laughter cottage throwing civil dejection happiness. Stanhill earnestly sorry september enjoy. Seemed neglected drew.  

Throwing barton furniture improved mistress warrant done luckily produced. Ourselves match would inquiry esteem. Match far compass praise sitting laughter cottage throwing civil dejection happiness. Stanhill earnestly sorry september enjoy. Seemed neglected drew.  

Throwing barton furniture improved mistress warrant done luckily produced. Ourselves match would inquiry esteem. Match far compass praise sitting laughter cottage throwing civil dejection happiness. Stanhill earnestly sorry september enjoy. Seemed neglected drew.  

Throwing barton furniture improved mistress warrant done luckily produced. Ourselves match would inquiry esteem. Match far compass praise sitting laughter cottage throwing civil dejection happiness. Stanhill earnestly sorry september enjoy. Seemed neglected drew.  

Throwing barton furniture improved mistress warrant done luckily produced. Ourselves match would inquiry esteem. Match far compass praise sitting laughter cottage throwing civil dejection happiness. Stanhill earnestly sorry september enjoy. Seemed neglected drew.  

Примем:
Х км/час скорость по шоссе;
32/Х время по шоссе;
(Х+20) скорость по автостраде;
60/(Х+20) время по автостраде.
Так как общее время = 1 час, составим и решим уравнение:
32/Х + 60/(Х+20) = 1;
приведем к общему знаменателю (Х*(Х+20)) и избавимся от него, умножив на него все члены уравнения:
32Х + 640 + 60Х = Х² + 20Х;
Х²-72Х - 640 = 0; 
Д=72²+4*640 = 5184+2560 = 7744; Д>0, продолжим;
Х₁ = (72 + √Д)/2 = (72 + √7744)/2 = (72+88)/2 = 80 (км/час);
Х₂ =72-√Д = -8 (в расчет не берем, как не имеющий смысла)
Х+20 = 80+20 = 100 (км/час);
ответ: скорость по шоссе 80км/час; скорость по автостраде 100 км/час;
Проверка: 32/80 +60/100 = 1; 0,4+0,6=1; 1=1