Tìm x `(x – 7)^{x + 1} – (x – 7)^{x + 11} = 0` 24/08/2021 Bởi Katherine Tìm x `(x – 7)^{x + 1} – (x – 7)^{x + 11} = 0`
Đáp án + Giải thích các bước giải: `(x-7)^{x+1}-(x-7)^{x+11}=0` `=>(x-7)^{x+11}-(x-7)^{x+1}=0` `=>(x-7)^{x+1}[(x-7)^{10}-1]=0` `=>` \(\left[ \begin{array}{l}(x-7)^{x+1}=0\\(x-7)^{10}-1=0\end{array} \right.\) `=>` \(\left[ \begin{array}{l}x-7=0\\(x-7)^{10}=1\end{array} \right.\) `=>` \(\left[ \begin{array}{l}x=7\\x-7=±1\end{array} \right.\) `=>` \(\left[ \begin{array}{l}x=7\\x=8\\x=6\end{array} \right.\) Vậy `x∈{6;7;8}` Bình luận
Đáp án: `x\in{6;7;8}` Giải thích các bước giải: `(x-7)^(x+1)-(x-7)^(x+11)=0``=>(x-7)^(x+1).1-(x-7)^(x+1).(x-7)^10=0``=>(x-7)^(x+1).[1-(x-7)^10]=0`TH`1``(x-7)^(x+1)=0``=>(x-7)^(x+1)=0^(x+1)``=>x-7=0``=>x=0+7``=>x=7`TH`2``1-(x-7)^10=0``=>(x-7)^10=1-0``=>(x-7)^10=1``=>x-7=+-1``=>`\(\left[ \begin{array}{l}x-7=1\\x-7=-1\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=8\\x6=\end{array} \right.\) Vậy `x\in{6;7;8}` Bình luận
Đáp án + Giải thích các bước giải:
`(x-7)^{x+1}-(x-7)^{x+11}=0`
`=>(x-7)^{x+11}-(x-7)^{x+1}=0`
`=>(x-7)^{x+1}[(x-7)^{10}-1]=0`
`=>` \(\left[ \begin{array}{l}(x-7)^{x+1}=0\\(x-7)^{10}-1=0\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x-7=0\\(x-7)^{10}=1\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=7\\x-7=±1\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=7\\x=8\\x=6\end{array} \right.\)
Vậy `x∈{6;7;8}`
Đáp án:
`x\in{6;7;8}`
Giải thích các bước giải:
`(x-7)^(x+1)-(x-7)^(x+11)=0`
`=>(x-7)^(x+1).1-(x-7)^(x+1).(x-7)^10=0`
`=>(x-7)^(x+1).[1-(x-7)^10]=0`
TH`1`
`(x-7)^(x+1)=0`
`=>(x-7)^(x+1)=0^(x+1)`
`=>x-7=0`
`=>x=0+7`
`=>x=7`
TH`2`
`1-(x-7)^10=0`
`=>(x-7)^10=1-0`
`=>(x-7)^10=1`
`=>x-7=+-1`
`=>`\(\left[ \begin{array}{l}x-7=1\\x-7=-1\end{array} \right.\)
`=>`\(\left[ \begin{array}{l}x=8\\x6=\end{array} \right.\)
Vậy `x\in{6;7;8}`