Question

cho X + \(\frac{1}{X}\) =3 tinh X⁵ + \(\frac{1}{X^5}\)

Answer 1

Ta có: \(\left(x+\frac{1}{x}\right)^3=x^3+\frac{3x^2}{x}+\frac{3x}{x^2}+\frac{1}{x^3}\)

\(x^3+\frac{1}{x^3}+3x+\frac{3}{x}=x^3+\frac{1}{x^3}+3\left(x+\frac{1}{x}\right)=27\)

\(x^3+\frac{1}{x^3}=18\)

Ta có:

\(\left(x+\frac{1}{x}\right)^5=x^5+\frac{5x^4}{x}+\frac{10x^3}{x^2}+\frac{10x^2}{x^3}+\frac{5x}{x^4}+\frac{1}{x^5}\)

\(x^5+\frac{1}{x^5}+5x^3+10x+\frac{10}{x}+\frac{5}{x^3}=243\)

\(x^5+\frac{1}{x^5}+5\left(x^3+\frac{1}{x^3}\right)+10\left(x+\frac{1}{x}\right)=243\)

\(x^5+\frac{1}{x^5}+5\left(x^3+\frac{1}{x^3}\right)=213\)

\(x^5+\frac{1}{x^5}=123\)