Question

Giai pt

a) \(x^2-5|x|-6=0\)

b)\(\dfrac{x}{x-2}+\dfrac{5}{|x+2|}=1\)

c)\(|x-2010|^{2011}+|x-2011|^{2010}=1\)

Answer 1

a: \(\Leftrightarrow\left(\left|x\right|\right)^2-5\left|x\right|-6=0\)

\(\Leftrightarrow\left(\left|x\right|-6\right)\left(\left|x\right|+1\right)=0\)

\(\Leftrightarrow\left|x\right|-6=0\)

=>x=6 hoặc x=-6

b: \(\dfrac{x}{x-2}+\dfrac{5}{\left|x+2\right|}=1\)

Trường hợp 1: x>-2 và x<>2

Pt sẽ là \(\dfrac{x}{x-2}+\dfrac{5}{x+2}=1\)

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)=x\left(x+2\right)+5\left(x-2\right)\)

\(\Leftrightarrow x^2+2x+5x-10=x^2-4\)

=>7x=6

hay x=6/7(nhận)

TRường hợp 2: x<-2

Pt sẽ là \(\dfrac{x}{x-2}-\dfrac{5}{x+2}=1\)

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)=x\left(x+2\right)-5\left(x-2\right)\)

\(\Leftrightarrow x^2+2x-5x+10=x^2-4\)

=>-3x=-14

hay x=14/3(loại)