Question

[Thiên Thần Bé Nhỏ]

1. Find the positive value of x such that:

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

2. Find the remainder of the division:

\(\left(x^3-13+5x-3x^2\right):\left(x-3\right)\)

Answer 1

[Nguyễn Lê Phước Thịnh]

Câu 1: 

\(\Leftrightarrow x^2-2x+1-2\left|x-1\right|-3=0\)

\(\Leftrightarrow\left(\left|x-1\right|\right)^2-2\left| x-1\right|-3=0\)

\(\Leftrightarrow\left(\left|x-1\right|-3\right)\left(\left|x-1\right|+1\right)=0\)

=>x-1=3 hoặc x-1=-3

=>x=4 hoặc x=-2