[VA] SRC #016 - Pi Day 2024 Special

[J-F Garnier]

(03-14-2024 06:20 PM)Valentin Albillo Wrote:  Solve the following equations, either using a program or directly from the keyboard. Remember, don't post just the result, include also the code or keystroke sequence:

• Fermat-like:
  
        2063^x + 8093^x = 8128^x
  
        1198^x + 4628^x = 4649^x
  

I like these two ones!

Here we are with \(\pi\) approximations, not exact value given by infinite series.

On the 71b:

>FROOT(1,6,2063^FX+8093^FX-8128^FX)
3.14159265353

>FROOT(1,6,1198^FX+4628^FX-4649^FX)
3.14159265363

Let's check the first equation on Free42:
LBL "P5"
MVAR "X"
2063
RCL "X"
Y^X
8093
RCL "X"
Y^X
+
8128
RCL "X"
Y^X
-
RTN

Solve it between 1 and 6, result is: 3.141592653590...
Not bad, almost correct to 13 digits.

Or in the other way:
PI , STO "X" , XEQ "P5" , result = 0.019368999924...

J-F