Forgot password
 Register account
original poster: kuing

来自人教群的 $5^x+2^y=2^x+5^y=7/10$

[Copy link]

84

Threads

2340

Posts

4

Reputation

Show all posts

其妙 posted 2013-12-27 12:34
回复  kuing

因为一直找不到不靠计算器证明最后那个数为正的办法,所以一直没放上来。 ...
爪机专用 发表于 2013-12-27 00:34
我们都知道,kk要求很严谨,

56

Threads

984

Posts

41

Reputation

Show all posts

乌贼 posted 2013-12-27 13:25
$5^x+2^y=\dfrac{7}{10}\riff5^x=\dfrac{7}{10}-2^y$
令$f_1(x)=5^x,g_1(y)=\dfrac{7}{10}-2^y$,知方程$5^x+2^y=\dfrac{7}{10}$的解即为$f_1,g_2$的交点(有唯一解)
同理
       $5^y+2^x=\dfrac{7}{10}\riff5^y=\dfrac{7}{10}-2^x$
令$f_2(y)=5^y,g_2(y)=\dfrac{7}{10}-2^x$,知方程$5^y+2^x=\dfrac{7}{10}$的解即为$f_2,g_2$的交点(有唯一解)
$f_1=f_2,g_1=g_2$有$x=y$……

0

Threads

406

Posts

6

Reputation

Show all posts

爪机专用 posted 2013-12-27 14:18
回复 22# 乌贼

不知道你在做什么

84

Threads

2340

Posts

4

Reputation

Show all posts

其妙 posted 2013-12-27 15:17
回复  乌贼

不知道你在做什么
爪机专用 发表于 2013-12-27 14:18
他在证明、但默认了$x=y$

56

Threads

984

Posts

41

Reputation

Show all posts

乌贼 posted 2013-12-27 20:11
回复 23# 爪机专用
我现在也不知道自己在干嘛

Quick Reply

Advanced Mode
B Color Image Link Quote Code Smilies
You have to log in before you can reply Login | Register account

$\LaTeX$ formula tutorial

Mobile version

2025-7-15 14:23 GMT+8

Powered by Discuz!

Processed in 0.012489 seconds, 21 queries