Question

Cho f(x) = \(x^{^{ }3}-6x+4\)

g(x)= \(x^3-4.\left(x+2\right)\)

Tìm x để \(\left|f\left(x\right)-g\left(x\right)\right|\) có giá trị nguyên không lớn hơn 1

Answer 1

\(f\left(x\right)-g\left(x\right)=x^3-6x+4-x^3+4x+8=-2x+12\)

Do \(\left|f\left(x\right)-g\left(x\right)\right|\le1\Rightarrow\left[{}\begin{matrix}\left|f\left(x\right)-g\left(x\right)\right|=0\\\left|f\left(x\right)-g\left(x\right)\right|=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}f\left(x\right)-g\left(x\right)=0\\f\left(x\right)-g\left(x\right)=1\\f\left(x\right)-g\left(x\right)=-1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}-2x+12=0\\-2x+12=1\\-2x+12=-1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=6\\x=\frac{11}{2}\\x=\frac{13}{2}\end{matrix}\right.\)