Question

\((x-1)^2+|x+21|-x^2-13=0\)

Answer 1

TH1: `x+21 >=0 <=> x >=-21`

`(x-1)^2+x+21-x^2-13=0`

`<=>x^2-2x+1+x+21-x^2-13=0`

`<=>-x=-9`

`<=>x=9 (TM)`

TH2: `x<-21`

`(x-1)^2-(x+21)-x^2-13=0`

`<=>-3x-33=0`

`<=>x=-11(L)`

Vậy `S={9}`.

 

Answer 2

\(\left(x-1\right)^2+\left|x+21\right|-x^2-13=0\)

\(\Leftrightarrow2x+12=\left|x+21\right|\) (*)

Do đó 2x + 12 \(\ge0\Leftrightarrow x\ge-6\).

Khi đó (*) \(\Leftrightarrow\left[{}\begin{matrix}x+21=2x+12\\x+21=-\left(2x+12\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=9\left(TM\right)\\x=-11\left(\text{\left\{loại\right\}}\right)\end{matrix}\right.\)