Question

Answer 1

Bài 1:

a: \(x^3+\dfrac{1}{x^3}=\left(x+\dfrac{1}{x}\right)^3-3\cdot x\cdot\dfrac{1}{x}\left(x+\dfrac{1}{x}\right)\)

\(=3^3-3\cdot3=27-9=18\)

b: x^2+1/x^2=14

=>(x+1/x)^2-2=14

=>(x+1/x)^2=16

=>x+1/x=4 hoặc x+1/x=-4

TH1: x+1/x=4

\(A=\left(x+\dfrac{1}{x}\right)^3-3\cdot x\cdot\dfrac{1}{x}\left(x+\dfrac{1}{x}\right)=\left(x+\dfrac{1}{x}\right)^3-3\left(x+\dfrac{1}{x}\right)\)

\(=4^3-3\cdot4=64-12=52\)

TH2: x+1/x=-4

\(A=\left(-4\right)^3-3\cdot\left(-4\right)=-64+12=-52\)