Post Go back to editing

# KCC's Quizzes AQQ253 about a funny equation

And here is a new challenge! It's easier than the previous one but still...

Also, please be informed awards and goodies are being sent to the frequent winners. Please apologize for the long delay since we do that only 2 times per year!

Certificates of the wins are also sent in paper form; the ones desiring a digital copy, please let us know!

Some statistics about the frequent winners by country origins: (we have also statistics by individuals, but they can be provided on demand and only with own data).

Regards

Kuo-Chang

Parents
• 8x+2x=130

(23)x+2x=130

(2x)3+2x=130

Let a=2x which results in the cubic equation:

a3+a-130=0

By inspection, the real root is a=5.  The two other roots are non-real complex conjugate numbers.  See Cardano’s formula in Wikipedia for the calculation of the complex roots.

X=log(a)/log(2)=2.321928095

• Correct! That equation accepts 3 solutions: one real and 2 complex. Congratulations

• If you calculate x from the complex solutions you express the numbers as |mag| times e^(iTheta).  Then you use the natural log (ln) to solve for x.  This results in an infinite number of answers separated by 2Pi.

• Indeed!