# Đại số lớp 7

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Tìm x biết:

a) ( x - 1)3 = 343

b)(x - 2)4 = 4069

c) ( x - 4)2 = ( x - 4)4

14 tháng 8 2017 lúc 20:41

a) $(x-1)^3$=343

$=>(x-1)^3=7^3$

$=>x-1=7$

$=>x=8$

b) (số sai rồi nha bạn, ra lẻ lắm)

c) $(x-4)^2=(x-4)^4$

$=>(x-4)^4-(x-4)^2=0$

$=>(x-4)^2[(x-4)^2-1]=0$

$=>\left[{}\begin{matrix}\left(x-4\right)^2=0\\\left(x-4\right)^2-1=0\end{matrix}\right.$

$=>\left[{}\begin{matrix}\left(x-4\right)^2=0\\\left(x-4\right)^2=1\end{matrix}\right.$

$=>\left[{}\begin{matrix}x-4=0\\x-4=1\\x-4=-1\end{matrix}\right.$

$=>\left[{}\begin{matrix}x=4\\x=5\\x=3\end{matrix}\right.$

14 tháng 8 2017 lúc 20:42

a,$\left(x-1\right)^3=343$

$\Rightarrow x-1=7\Rightarrow x=8$

b, $\left(x-2\right)^4=4096$

$\Rightarrow x-2=8\Rightarrow x=10$

c, $\left(x-4\right)^2=\left(x-4\right)^4$

$\Rightarrow\left(x-4\right)^2=\left[\left(x-4\right)^2\right]^2$

$\Rightarrow x-4=\left(x-4\right)^2$

$\Rightarrow\left(x-4\right)-\left(x-4\right)^2=0$

$\Rightarrow\left(x-4\right)\left(1-x+4\right)=0$

$\Rightarrow\left[{}\begin{matrix}x-4=0\\5-x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=5\end{matrix}\right.$

Chúc bạn học tốt!!!

14 tháng 8 2017 lúc 20:44

$\left(x-1\right)^3=343$

$\Rightarrow\left(x-1\right)^3=7^3$

$\Rightarrow x-1=7\Rightarrow x=8$

$\left(x-2\right)^4=4096$

$\Rightarrow\left(x-2\right)^4=\pm8^4$

$\Rightarrow\left[{}\begin{matrix}x-2=8\Rightarrow x=10\\x-2=-8\Rightarrow x=-6\end{matrix}\right.$

$\left(x-4\right)^2=\left(x-4\right)^4$

$\Rightarrow\left(x-4\right)^4-\left(x-4\right)^2=0$

$\Rightarrow\left(x-4\right)^2\left[\left(x-4\right)^2-1\right]=0$

$\Rightarrow\left\{{}\begin{matrix}\left(x-4\right)^2=0\\\left(x-4\right)^2=1\end{matrix}\right.$

$\Rightarrow x=4$

$\Rightarrow\left\{{}\begin{matrix}x-4=1\Rightarrow x=5\\x-4=-1\Rightarrow x=3\end{matrix}\right.$

14 tháng 8 2017 lúc 20:48

$a,\left(x-1\right)^3=343$

$\Leftrightarrow\left(x-1\right)^3=7^3$

$\Leftrightarrow x-1=7$

$\Leftrightarrow x=8$

Vậy ........

b) $\left(x-2\right)^4=4069$

$\Leftrightarrow\left(x-2\right)^4=8^4$

$\Leftrightarrow x-2=8$

$\Leftrightarrow x=10$

Vậy ..............

c) $\left(x-4\right)^2=\left(x-4\right)^4$

$\Leftrightarrow\left(x-4\right)^2=\left[\left(x-4\right)^2\right]^2$

$\Leftrightarrow x-4=\left(x-4\right)^2$

$\Leftrightarrow\left(x-4\right)-\left(x-4\right)^2=0$

$\Leftrightarrow x-4-\left(1-x+4\right)=0$

$\Leftrightarrow\left[{}\begin{matrix}x-4=0\\5-x=0\end{matrix}\right.$ $\Leftrightarrow\left[{}\begin{matrix}x=4\\x=5\end{matrix}\right.$

Vậy ...

14 tháng 8 2017 lúc 20:52

a) $\left(x-1\right)^3=343$

$\Leftrightarrow\left(x-1\right)^3=7^3$

$\Leftrightarrow x-1=7\Leftrightarrow x=8$

Vậy x = 8.

b) $\left(x-2\right)^4=4096$

$\Leftrightarrow\left[{}\begin{matrix}x-2=8\\x-2=-8\end{matrix}\right.$

$\Leftrightarrow\left[{}\begin{matrix}x=10\\x=-6\end{matrix}\right.$

Vậy x1 = 10; x2 = -6.

c) $\left(x-4\right)^2=\left(x-4\right)^4$

$\Leftrightarrow\left(x-4\right)^2-\left(x-4\right)^4=0$

$\Leftrightarrow\left(x-4\right)^2\left[1-\left(x-2\right)^2\right]=0$

$\Leftrightarrow\left(x-4\right)^2\left(1-x+2\right)\left(1+x-2\right)=0$

$\Leftrightarrow\left(x-4\right)^2\left(3-x\right)\left(x-1\right)=0$

$\Leftrightarrow\left[{}\begin{matrix}\left(x-4\right)^2=0\\3-x=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=3\\x=1\end{matrix}\right.$

Vậy x1 = 4; x2 = 3; x3 = 1.

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