How do you solve 36x2+9=216x2+9?
1 Answer
May 22, 2017
for any integer
Explanation:
Given:
36x2+9=216x2+9
Divide both sides by
1=6x2+9=e(x2+9)ln6
From Euler's identity we can deduce:
(x2+9)ln6=2kπi
for any integer
So:
x2+9=2kπiln6
Hence:
x=±√2kπiln6−9
If
x=±√−9=±3i
Footnote
If you would like the other roots in
±⎛⎝⎛⎝√√a2+b2+a2⎞⎠+⎛⎝b|b|√√a2+b2−a2⎞⎠i⎞⎠