Question

Tìm hàm số y=f(x) thoã mãn:

\(f\left(x+\dfrac{1}{x}\right)\)=\(x^3+\dfrac{1}{x^3}\)

Answer 1

\(f\left(x+\dfrac{1}{x}\right)=x^3+\dfrac{1}{x^3}=\left(x+\dfrac{1}{x}\right)\left(x^2-1+\dfrac{1}{x^2}\right)\)

\(f\left(x+\dfrac{1}{x}\right)=\left(x+\dfrac{1}{x}\right)\left(x^2+2x.\dfrac{1}{x}+\dfrac{1}{x^2}-3\right)\)

\(f\left(x+\dfrac{1}{x}\right)=\left(x+\dfrac{1}{x}\right)\left[\left(x+\dfrac{1}{x}\right)^2-3\right]\)

vậy \(f\left(x\right)=x\left(x^2-3\right)=x^3-3x\)