Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Find the nth roots of the equation?
(z+1)^n = 3 (z+2)^n
I appreciate all help! Thanks in advance.
1 Answer
- RaymondLv 76 years ago
If you took the "n"th root on both sides, you would be left with the roots themselves (as if n=1)
n=1
z+1 = 3(z+2)
z + 1 = 3z + 6
-5 = 2z
-5/2 = z
This (n=1) is what you would have if you took the "n"th root on both sides, in real numbers.
-----
If you tried to solve directly for specific values of n, you would begin with small values:
If n=0 then we have
1 = 3
This is not good.
-----
n = 2
z^2 + 2z + 1 = 3(z^2 + 4z + 4)
z^2 + 2z + 1 = 3z^2 + 12z + 12
0 = 2z^2 + 10z + 3
Quadratic formula
z = [ -10 ± √(100 - 24)¸/ 4
z = [ -10 ± √(76)] / 4
z = -5/2 ± √(4.75)
It seems the value of z depends on the value of n.
