How do you solve 36x2+9=216x2+9?

1 Answer
May 22, 2017

x=±2kπiln69

for any integer k

Explanation:

Given:

36x2+9=216x2+9

Divide both sides by 36x2+9 to get:

1=6x2+9=e(x2+9)ln6

From Euler's identity we can deduce:

(x2+9)ln6=2kπi

for any integer k

So:

x2+9=2kπiln6

Hence:

x=±2kπiln69

If k=0 that gives us:

x=±9=±3i


Footnote

If you would like the other roots in a+bi form, then you can use the formula derived in https://socratic.org/s/aEUsUcjD , namely that the square roots of a+bi are:

±a2+b2+a2+b|b|a2+b2a2i