Question

Tìm x biết:

6xⁿ⁺² - 4xⁿ+3xⁿ⁺² - 5xⁿ +xⁿ⁺² - xⁿ = 0 (n thuộc N*)

Giúp mk nha, thanks trước

Answer 1

\(6x^{n+2}-4x^n+3x^{n+2}-5x^n+x^{n+2}-x^n=0\)

\(\left(6x^{n+2}+3x^{n+2}+x^{n+2}\right)+\left(-4x^n-5x^n-x^n\right)=0\)

\(x^{n+2}\left(6+3+1\right)+x^n\left(-4-5-1\right)=0\)

\(10x^{n+2}+\left(-10\right)x^n=0\)

\(10x^n.x^2+\left(-10\right)x^n=0\)

\(x^n\left(10x^2-10\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x^n=0\\10x^2-10=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\left(n\in N\circledast\right)\\10x^2=10\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x^2=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\\left\{{}\begin{matrix}x=-1\\x=1\end{matrix}\right.\end{matrix}\right.\)

Vậy...