SOLUTION: Solve the equation for the value of n: {{{x^(n-1)+x^(n+1)=320}}} My approach was {{{x^(n-1)+x^(n+1)=320}}} {{{x^(n-1)+x^(n+1)=256+64}}} {{{x^(n-1)+x^(n+1)=2^6+2^8}}} So

Algebra.Com
Question 1151635: Solve the equation for the value of n:
My approach was




So,


Can I solve the question this way ? If not , please solve it in the right way . Thanks

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Let start discussing the problem's formulation.


If you allow x and "n" to be any real numbers, then, probably, other solutions (non-integer, rational or irrational) may exist.


But, probably, the problem restricts you by integer values of x and "n" --- it would be very natural.


So, let's assume that we are looking for integer positive x and "n", only.


Then your approach is only PARTLY good : you just found one solution, but you did not guarantee that there is no other solution.

In your post, you even did not touch this issue.


In this sense, your solution is not complete.


There is another approach.


The starting equation can be transformed into other, equivalent equation


     = 320

     = .


Having it in this form, it is easy to prove that the only solution is


    x = 2, n = 7,


using the divisibility properties of integer numbers.


At this point I'd like to complete my explanation.



RELATED QUESTIONS

Simplify... (answered by Alan3354)
log... (answered by mukhopadhyay)
x(m+n+1) (answered by robertb)
(X^n-3)(2x^n+5)÷x^(n-1) (answered by solver91311)
solve for n, where: X =... (answered by josgarithmetic)
find the general solution for x(n)and y(n)for x(0)=1 and y(0)=0, x(n+1)=x(n)+2y(n)... (answered by rapaljer)
1. Let X(k) denote the N-point DFT of the N-point sequence x(n) a) If x(n)... (answered by Fombitz)
Simplify: 2^n+1 (x+3)^n --------------------- 2^n (x+3)^n-1 (answered by sofiyac)
Solve for x if ax^n +... (answered by MathLover1)