Đáp án:
`1. ((-3)^(201)-81)/(-4)`
`2. a)` \(\left[ \begin{array}{l}x=3\\x=4\end{array} \right.\)
`b) `\(\left[ \begin{array}{l}x=2\\x=5\end{array} \right.\)
Giải thích các bước giải:
`C=3^4+(-3)^5+...+(-3)^(201)`
`C=(-3)^4+ (-3)^5+...+(-3)^(201)`
`(-3).C=(-3)^5+(-3)^6+...+(-3)^(201)`
`(-3).C-C=[(-3)^5+(-3)^6+...+(-3)^(201)]-[(-3)^4+ (-3)^5+...+(-3)^(201)]`
`(-4).C=(-3)^(201)-81`
`C=((-3)^(201)-81)/(-4)`
`2)`
`a) (x-3)^(206)=|x-3|`
`=> (x-3)^(206)-|x-3|=0`
`=> (x-3)[(x-3)^(205)-1]=0`
`=>` \(\left[ \begin{array}{l}x-3=0\\(x-3)^(205)-1=0\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=3\\(x-3)^(205)=1\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=3\\x-3=1\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=3\\x=4\end{array} \right.\)
`b) (x-2)(2x-10)=0`
`=>` \(\left[ \begin{array}{l}x-2=0\\2x-10=0\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=2\\x=5\end{array} \right.\)
