Question

Tìm x thuộc Z biết

a. \(\left(x-1\right)\times\left(2x-4\right)=0\)

b. \(\left(x^2+5\right)\times\left(x-5\right)=0\)

c. \(\left(x^2+5\right)\times\left(x^2-2\right)=0\)

d. \(\left(x^2-1\right)\times\left(x^2-9\right)< 0\)

e. \(\left|x^2-2x\right|=x\)

g. \(\left|2x+1\right|+\left|x+8\right|=4x\)

Answer 1

a) \(\left(x-1\right)\left(2x-4\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-1=0\Rightarrow x=1\\2x-4=0\Rightarrow x=2\end{matrix}\right.\)

b) \(\left(x^2+5\right)\left(x-5\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x^2+5=0\Rightarrow x=-\sqrt{5}\\x-5=0\Rightarrow x=5\end{matrix}\right.\)

mà \(x\in Z\Rightarrow x=5\)

c) \(\left(x^2+5\right)\left(x^2-2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x^2+5=0\Rightarrow x=-\sqrt{5}\\x^2-2=0\Rightarrow x=\sqrt{2}\end{matrix}\right.\)

mà \(x\in Z\Rightarrow x\in\varnothing\)