$\color{blue}{\boxed{\color{red}{(} \color{#FF5500}{っ} \color{#FFAA00}{◔} \color{#FFFF00}{◡} \color{#AAFF00}{◔} \color{#55FF00}{)} \color{#00FF00}{っ} \color{#00FF55}{ ♥}\begin{matrix}\color{#00FFAA}{t}\color{#00FFFF}{r} \color{#00AAFF}{i} \color{#0055FF}{e}\color{#0000FF}{t} \color{#5500FF}{s} \color{#AA00FF}{i} \color{#FF00FF}{g} \color{#FF00AA}{a} \color{#FF0055}{i}\\\color{#00FFAA}{♥} \color{#00FFFF}{♥} \color{#00AAFF}{♥} \color{#0055FF}{♥}\color{#0000FF}{♥} \color{#5500FF}{♥} \color{#AA00FF}{♥} \color{#FF00FF}{♥} \color{#FF00AA}{♥} \color{#FF0055}{♥}\\\color{#00FFAA}{n} \color{#00FFFF}{h} \color{#00AAFF}{i} \color{#0055FF}{x}\color{#0000FF}{i} \color{#5500FF}{n} \color{#AA00FF}{h} \color{#FF00FF}{i} \color{#FF00AA}{u}\end{matrix}}}$

`|x^2-1|+|x+1|=0`

`|(x-1)(x+1)|+|x+1|=0`

`|x-1|.|x+1|+|x+1|=0`

`|x+1|.(|x-1|+1)=0`

+) `|x+1|=0`

`\Rightarrow x=-1`

+) `|x-1|+1=0` 

Vì `|x-1|\ge 0\forall x\in\mathbb{R}`

`\Rightarrow |x-1|+1\ge 1\ne 0`

Vậy phương trình có 1 nghiệm duy nhất là `x=-1`

$\begin{matrix}\color{#00FF55}{ ♥}\\\color{#00FF55}{ ♥}\\\color{#00FF55}{ ♥}\end{matrix}\begin{matrix}\color{#00FFAA}{♥} \color{#00FFFF}{♥} \color{#00AAFF}{♥} \color{#0055FF}{♥}\color{#0000FF}{♥} \color{#5500FF}{♥} \color{#AA00FF}{♥} \color{#FF00FF}{♥} \color{#FF00AA}{♥} \color{#FF0055}{♥}\\\color{#00FFAA}{t}\color{#00FFFF}{r} \color{#00AAFF}{i} \color{#0055FF}{e}\color{#0000FF}{t} \color{#5500FF}{s} \color{#AA00FF}{i} \color{#FF00FF}{g} \color{#FF00AA}{a} \color{#FF0055}{i}~~~~\color{#FF0055}{♥}\\\color{#00FFAA}{♥} \color{#00FFFF}{♥} \color{#00AAFF}{♥} \color{#0055FF}{♥}\color{#0000FF}{♥} \color{#5500FF}{♥} \color{#AA00FF}{♥} \color{#FF00FF}{♥} \color{#FF00AA}{♥} \color{#FF0055}{♥}\end{matrix}$