07 Jan Solving a cubic expression with two x variables.

The first time a saw this expression it looked unsolvable and more like a riddle. That is to my layman’s eyes off course. Experienced mathematicians solve it during a morning jog. Anyway, it looked challenging enough. Sometimes the simplest things are the hardest to solve.

\(\large x^4 = 2^x \)

In order to solve this expression we need to set it to equal zero.

\(\large x^4 – 2^x = 0 \)

[f][R↓]	
[g][R/S]
[f][SST]C
[4][yx][X<>Y]
[2][X<>Y][yx][-]
[g][GSB]
[g][R/S]

There are actually two roots. With a little insight to your equation, you can get acurate solutions. To solve for the lower root we enter the following key sequence:

[0][ENTER]
[2][0]
[f][SOLVE][C]

First root is -0.8613

To find the second root change the range:

[1][0][ENTER]
[2][0]
[f][SOLVE][C]

The answer should be 16

Enjoy!

Acknowledgment:

I have to admit I got stuck with this small program for several months. After so many futile attempts I thought to get help from Edward Shore. He gracefully helped me via email where I went wrong. So thank you Eddie, it is highly appreciated. Visit Eddies math website at: http://edspi31415.blogspot.com