+0  
 
+1
197
4
avatar+383 

Solve x! + 2x = 104

 

to one decimal place, using trial and improvement

 May 4, 2020
 #1
avatar+112302 
+2

Haven't seen one like this before....

 

Note that  4!   =  24

And 5!  =  120

 

So...we might guess that  x   falls between these two values

 

4.8! + 2(4.8)  =  95.198

 

4.9!  + 2(4.9)  = 111.04

 

Test some values  for  x   in  x! + 2x

 

x             result

4.81      96.66

4.85      102.77

4.86      104.36

 

It appears  that  4.8  is what we need

 

BTW....WolframAlpha  shows the result to be  x  ≈ 4.858

 

cool cool cool

 May 4, 2020
 #2
avatar+652 
+3

Nice solution!

LuckyDucky  May 4, 2020
 #3
avatar+383 
0

wait so its 4.8 or 4.86? or 4.858

TacoBell  May 4, 2020
 #4
avatar+112302 
+1

We only want one decimal place

 

So...   4.8

 

 

cool cool cool

CPhill  May 4, 2020

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