Question

x+1/x=3 . Tính x^2+1/x^2

 

Answer 1

ĐK : x ≠ 0

\(\dfrac{x+1}{x}=3\)

=> \(3x=x+1\)

=> \(2x=1\)

=> \(x=\dfrac{1}{2}\)

=> \(x^2=\dfrac{1}{4}\)

=> \(\dfrac{1}{x^2}=4\)

Khi đó

\(\dfrac{x^2+1}{x^2}=1+\dfrac{1}{x^2}=1+4=5\)

Answer 2

\(x+\dfrac{1}{x}=3\Rightarrow x^2+\dfrac{1}{x^2}+2.x.\dfrac{1}{x}=9\Rightarrow x^2+\dfrac{1}{x^2}=7\)