Interesting Property

Algebra Level 1

x n + x n = x n + 1 x^{n}+x^{n}=x^{n+1}

If x x is a positive integer, then solve for x x .


The answer is 2.

Blan Morrison by Blan Morrison , 18, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Blan Morrison
Dec 14, 2017

Relevant wiki: Rules of Exponents - Algebraic

  1. Combine like terms: 2 x n = x n + 1 2x^{n}=x^{n+1}

  2. Divide both sides by x n x^{n} : 2 x n x n \frac{2x^{n}}{x^{n}} = x n + 1 x n \frac{x^{n+1}}{x^{n}} .

  3. Simplify by using the rules of exponents: 2 = x 2=x . β ⌈ ∣ ⌉ ~\beta_{\lceil \mid \rceil}

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Munem Shahriar
Feb 28, 2018

x n + x n = x n + 1 x n = x n + 1 − x n x n = x n ( x − 1 ) 1 = x − 1 1 + 1 = x \begin{aligned} x^n + x^n & = x^{n+1} \\ x^n & = x^{n+1} - x^n \\ x^n & = x^n(x-1) \\ 1 & = x-1 \\ 1 + 1 & = x \\ \end{aligned}

⟹ x = 2 \implies x = \boxed 2

1 Helpful 0 Interesting 1 Brilliant 0 Confused
Edwin Gray
Oct 28, 2018

x^n + x^n = 2x^n = x^(n+1) = x*x^n. Divide by x^n, x = 2. Ed Gray

0 Helpful 0 Interesting 0 Brilliant 2 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...