tìm x biết : $(x-7)^{x+1}$ – $(x-7)^{x+11}$ =0 08/11/2021 Bởi aikhanh tìm x biết : $(x-7)^{x+1}$ – $(x-7)^{x+11}$ =0
Đáp án: $\left[ \begin{array}{l}x=7\\x=8\\x=6\end{array} \right.$ Giải thích các bước giải: $(x-7)^{x+1}-(x-7)^{x+11}=0$ $⇔(x-7)^{x+1}-(x-7)^{x+1}.(x-7)^{10}=0$ $⇔(x-7)^{x+1}.[1-(x-7)^{10}]=0$ $⇔\left[ \begin{array}{l}(x-7)^{x+1}=0\\1-(x-7)^{10}=0\end{array} \right.$ $⇔\left[ \begin{array}{l}x-7=0\\x-7=1\\x-7=-1\end{array} \right.$ $⇔\left[ \begin{array}{l}x=7\\x=8\\x=6\end{array} \right.$ Bình luận
(x – 7)^x + 1 – (x – 7)^x + 11 = 0 (x – 7)^x . (x – 7) – (x – 7)^x . (x – 7)^11 = 0 (x – 7)^x . [(x – 7) – (x – 7)^11] = 0 => (x – 7)^x = 0 hoặc [(x – 7) – (x – 7)^11] = 0 * TH1: (x – 7)^x = 0 => x – 7 = 0 => x = 0 + 7 => x = 7 * TH2: [(x – 7) – (x – 7)^11] = 0=> x – 7 = (x -7)^11=> x – 7 = 1 hoặc x – 7 = 0x – 7 = 1=> x = 1 + 7 x = 8x – 7 = 0 (TH1) Vậy x = 7 hoặc x = 8. Bình luận
Đáp án:
$\left[ \begin{array}{l}x=7\\x=8\\x=6\end{array} \right.$
Giải thích các bước giải:
$(x-7)^{x+1}-(x-7)^{x+11}=0$
$⇔(x-7)^{x+1}-(x-7)^{x+1}.(x-7)^{10}=0$
$⇔(x-7)^{x+1}.[1-(x-7)^{10}]=0$
$⇔\left[ \begin{array}{l}(x-7)^{x+1}=0\\1-(x-7)^{10}=0\end{array} \right.$
$⇔\left[ \begin{array}{l}x-7=0\\x-7=1\\x-7=-1\end{array} \right.$
$⇔\left[ \begin{array}{l}x=7\\x=8\\x=6\end{array} \right.$
(x – 7)^x + 1 – (x – 7)^x + 11 = 0
(x – 7)^x . (x – 7) – (x – 7)^x . (x – 7)^11 = 0
(x – 7)^x . [(x – 7) – (x – 7)^11] = 0
=> (x – 7)^x = 0 hoặc [(x – 7) – (x – 7)^11] = 0
* TH1: (x – 7)^x = 0
=> x – 7 = 0
=> x = 0 + 7
=> x = 7
* TH2: [(x – 7) – (x – 7)^11] = 0=> x – 7 = (x -7)^11=> x – 7 = 1 hoặc x – 7 = 0x – 7 = 1=> x = 1 + 7 x = 8x – 7 = 0 (TH1)
Vậy x = 7 hoặc x = 8.