$n^3=n, n^2 \not= n$

Algebra Level 1

What is a number whose cube is equal to the number itself but its square is not equal to the number itself?

$\huge{n^3=n, n^2 \not= n}$

2 solutions

Cera Mess
Mar 20, 2018

Let the number be $\color{limegreen}{x}$

$\color{#D61F06}{x^3 = x}$ but $\color{#EC7300}{x^2 \not= x}$

so $\color{#D61F06}{x^3-x=0}$ but $\color{#EC7300}{x^2-x \not= 0}$

$\color{#D61F06}{x(x^2-1)=0}$ but $\color{#EC7300}{x(x-1)\not= 0}$

$\color{#D61F06}{x(x+1)(x-1)=0}$ but $\color{#EC7300}{x(x-1)\not= 0}$

$\color{#D61F06}{x = 0}$ or $\color{#D61F06}{1}$ or $\color{#D61F06}{-1}$ but $\color{#EC7300}{x \not= 0}$ or $\color{#EC7300}{1}$

so $\color{limegreen}{x}$ must be $\color{limegreen}{-1}$

Well done @CeraMess, I was still understanding the language by the time you finished the problem.

The Strategy Gamer - 3 years, 2 months ago

Your logical brain made my head hurt on this misty Wednesday night. <smile>

Joms Joseph Leelin - 3 years, 2 months ago

Why can’t you be my algebra tutor?

Jeff Ishee - 3 years, 2 months ago

Very good.

Rafael Melo - 3 years, 2 months ago

Well did .

That is a logical solution .

Ram Mohith - 3 years, 2 months ago

Vitor Juiz
Mar 20, 2018