
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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May 26th, 2019, 10:07 PM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 547 Thanks: 83  Number of solutions
Given equation(with respect to x): $\displaystyle x^n +x=nx $ , how many real solutions the equation has ? $\displaystyle x\geq 0 \; $ and $\displaystyle n\in \mathbb{N} $. 
May 27th, 2019, 01:55 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,819 Thanks: 2158 
2

May 28th, 2019, 07:07 AM  #3 
Senior Member Joined: Dec 2015 From: somewhere Posts: 547 Thanks: 83 
By factorization of the equation : $\displaystyle n\cdot x $ is totally independent to a constant . So the number of real solutions is 2. 
May 28th, 2019, 11:13 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,819 Thanks: 2158 
Your reasoning is unclear. Does it always apply?

May 29th, 2019, 12:42 AM  #5 
Senior Member Joined: Dec 2015 From: somewhere Posts: 547 Thanks: 83  
May 29th, 2019, 05:42 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,819 Thanks: 2158 
How exactly do you proceed in that way to your conclusion?


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