Answer:
Step-by-step explanation:
Let's begin by factoring x^2 + 9x - 10
When you do that you get
(x - 1) (x + 10)
If that can be done then let x^(2n) + 9^n - 10 be factored into
(x^n - 1) (x^n + 10) Both of these can be equated to zero.
x^n - 1 = 0
x^n = 1
Take the nth root of both sides
No matter what n is the root of 1 is still going to be 1
x^n + 10 = 0
x^n = - 10
This one is a little harder. It depends whether n is odd or even. It it is odd, no problem. The nth root of - 10 can be found.
For example, suppose n = 5. Then the 5th root of -10 is - 1.58
You can find this on your calculator by doing
(-)
10
y^x or x^y or ^ [whichever your calculator has]
=
and you should get - 1.58
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If n is even, you have a problem. If you do not know what complex numbers are, they this problem has not meaning. If n = 6, then you can take the sixth of 10. Then the answer becomes If you do know what then the answer becomes 1.468i. I would say if n is even there is no solution.
