Question

c) Cho 𝑥 + 1 /𝑥 = −4. Tính 𝑥^ 2 + 1 /𝑥^ 2

Answer 1

\(\dfrac{x+1}{x}=-4\Leftrightarrow-4x=x+1\Leftrightarrow x=-\dfrac{1}{5}\\ \dfrac{x^2+1}{x^2}=\dfrac{\dfrac{1}{25}+1}{\dfrac{1}{25}}=\dfrac{26}{25}\cdot25=26\)

Answer 2

\(x^2+\dfrac{1}{x^2}=\left(x^2+2+\dfrac{1}{x^2}\right)^2-2=\left(x+\dfrac{1}{x}\right)^2-2=\left(-4\right)^2-2=14\)