giúp e với e camon
Bài 5:
\(5^{n+2}+26.5^n+8^{2n+1}\)
\(=25.5^n+26.5^n+8.64^n\)
\(=51.5^n+8.64^n\)
\(=51.5^n+8.5^n+8.64^n-8.5^n\)
\(=59.5^n+8\left(64^n-5^n\right)\)
Ta thấy: \(\left\{{}\begin{matrix}59.5^n⋮59\\8\left(64^n-5^n\right)⋮\left(64-5\right)=59\end{matrix}\right.\)
⇒ \(59.5^n+8\left(64^n-5^n\right)⋮59\)
⇒ \(5^{n+2}+26.5^n+8^{2n+1}\) ⋮ \(59\)
⇒ \(ĐPCM\)
Câu 1:
1) b.
Ta có: \(P=-\dfrac{1}{2}\)
⇔ \(\dfrac{x^2}{x-1}=-\dfrac{1}{2}\)
⇒ \(2x^2=1-x\)
\(\Leftrightarrow2x^2+x-1=0\)
\(\Leftrightarrow2x^2+2x-x-1=0\)
⇔ \(2x\left(x+1\right)-\left(x+1\right)=0\)
⇔ \(\left(x+1\right)\left(2x-1\right)=0\)
⇒ \(\left[{}\begin{matrix}x+1=0\\2x-1=0\end{matrix}\right.\) ⇔ \(\left[{}\begin{matrix}x=-1\\x=\dfrac{1}{2}\end{matrix}\right.\)
Vậy khi \(P=-\dfrac{1}{2}\) thì \(x=-1\) hoặc \(x=\dfrac{1}{2}\)
