Discuz Math Forum»Forum › Mathematics › High School › 三次函数上任意两点的中点的集合

Return to list New

View 277|Reply 1

[几何] 三次函数上任意两点的中点的集合

[Copy link]

3214 Threads	7831 Posts	52 Reputation

Send PM

hbghlyj posted 2024-4-12 22:19 |Read mode

$y=x^3-x$上任意两点的中点的集合是整个平面吗？

Related threads

Reply Edit 0

3214 Threads	7831 Posts	52 Reputation

Send PM

original poster hbghlyj posted 2024-4-12 22:33

是平面被$y=x^3-x$的图象和y轴划分的区域

$$x(y-(x^3-x))>0$$
也可以写成\[
\frac{y}{x}>x^2-1
\]
Discriminant[(2x-t)^3-(2x-t)-(2y-t^3+t),t]>0

Reply Edit

Return to list New

Quick Reply

× Quick Reply To Top Edit

2025-7-20 13:46 GMT+8

Powered by Discuz!

Processed in 0.016855 seconds, 39 queries