Question

Biết x+ (1/x) =3. Giá trị của biểu thức x⁴+ (1/ x⁴) là bao nhiêu ?

Answer 1

ta có:   \(x+\frac{1}{x}=3\)

\(\Rightarrow\left(x+\frac{1}{x}\right)^2=3^2\)

\(\Leftrightarrow x^2+2.x.\frac{1}{x}+\left(\frac{1}{x}\right)^2=9\)

\(\Leftrightarrow x^2+2+\frac{1}{x^2}=9\)

\(\Leftrightarrow x^2+\frac{1}{x^2}=7\)

\(\Rightarrow\left(x^2+\frac{1}{x^2}\right)^2=7^2\)

\(\Leftrightarrow\left(x^2\right)^2+2.x^2.\left(\frac{1}{x^2}\right)+\left(\frac{1}{x^2}\right)^2=49\)

\(\Leftrightarrow x^4+2+\frac{1}{x^4}=49\)

\(\Leftrightarrow x^4+\frac{1}{x^4}=47\)

Answer 2

\(x+\frac{1}{x}=3\Rightarrow\left(x+\frac{1}{x}\right)^2=x^2+2+\frac{1}{x^2}=9\Rightarrow x^2+\frac{1}{x^2}=7\)

\(\Rightarrow\left(x^2+\frac{1}{x^2}\right)^2=x^4+2+\frac{1}{x^4}=49\Rightarrow x^4+\frac{1}{x^4}=47\)

Answer 3

cảm ơn các bạn !