(x – 8) ^ (2x + 2) = (8 – x) ^ (2x + 10) 31/10/2021 Bởi Valentina (x – 8) ^ (2x + 2) = (8 – x) ^ (2x + 10)
Đáp án + Giải thích các bước giải: Ta có : `(x-8)^{2x+2}=(8-x)^{2x+10}` `→(x-8)^{2x+2}-(x-8)^{2x+10}=0` `→(x-8)^{2x+2}[1-(x-8)^{8}]=0` `→` \(\left[ \begin{array}{l}(x-8)^{2x+2}=0\\1-(x-8)^{8}=0\end{array} \right.\) `→` \(\left[ \begin{array}{l}x-8=0\\(x-8)^{8}=1\end{array} \right.\) `→` \(\left[ \begin{array}{l}x=8\\x-8=1\\x-8=-1\end{array} \right.\) `→` \(\left[ \begin{array}{l}x=8\\x=9\\x=7\end{array} \right.\) Vậy `x∈{8;9;7}` Bình luận
$(x-8)^{2x + 2} = (8-x)^{2x+10}$ $⇒ (x-8)^{2x+2} – (8-x)^{2x+10}= 0$ $⇒ (x-8)^{2x+2} . [1-(x-8)^{8}] = 0$ $⇒ \left[ \begin{array}{l}(x-8)^{2x+2} = 0\\1-(x-8)^{8} = 0\end{array} \right.$ $⇒ \left[ \begin{array}{l}(x-8)= 0\\(x-8)^{8} = 1\end{array} \right.$ $⇒ \left[ \begin{array}{l}x=8\\x-8=1\\x-8=-1\end{array} \right.$ $⇒ \left[ \begin{array}{l}x=8\\x=9\\x=7\end{array} \right.$ Bình luận
Đáp án + Giải thích các bước giải:
Ta có :
`(x-8)^{2x+2}=(8-x)^{2x+10}`
`→(x-8)^{2x+2}-(x-8)^{2x+10}=0`
`→(x-8)^{2x+2}[1-(x-8)^{8}]=0`
`→` \(\left[ \begin{array}{l}(x-8)^{2x+2}=0\\1-(x-8)^{8}=0\end{array} \right.\)
`→` \(\left[ \begin{array}{l}x-8=0\\(x-8)^{8}=1\end{array} \right.\)
`→` \(\left[ \begin{array}{l}x=8\\x-8=1\\x-8=-1\end{array} \right.\)
`→` \(\left[ \begin{array}{l}x=8\\x=9\\x=7\end{array} \right.\)
Vậy `x∈{8;9;7}`
$(x-8)^{2x + 2} = (8-x)^{2x+10}$
$⇒ (x-8)^{2x+2} – (8-x)^{2x+10}= 0$
$⇒ (x-8)^{2x+2} . [1-(x-8)^{8}] = 0$
$⇒ \left[ \begin{array}{l}(x-8)^{2x+2} = 0\\1-(x-8)^{8} = 0\end{array} \right.$
$⇒ \left[ \begin{array}{l}(x-8)= 0\\(x-8)^{8} = 1\end{array} \right.$
$⇒ \left[ \begin{array}{l}x=8\\x-8=1\\x-8=-1\end{array} \right.$
$⇒ \left[ \begin{array}{l}x=8\\x=9\\x=7\end{array} \right.$