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a) \(\left(x-5\right)^{12}=\left(x-5\right)^{10}\)
\(\Rightarrow\left(x-5\right)^{12}-\left(x-5\right)^{10}=0\)
\(\Rightarrow\left(x-5\right)^{10}\left[\left(x-5\right)^2-1\right]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(x-5\right)^{10}=0\\\left(x-5\right)^2-1=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}\left(x-5\right)^{10}=0^{10}\\\left(x-5\right)^2=0+1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-5=0\\\left(x-5\right)^2=1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0+5\\\left(x-5\right)^2=1^2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=5\\x-5=\pm1\end{cases}}\)
\(\Rightarrow x=5;\orbr{\begin{cases}x-5=1\\x-5=-1\end{cases}}\)
\(\Rightarrow x=5;\orbr{\begin{cases}x=1+5\\x=-1+5\end{cases}}\)
\(\Rightarrow x=5;\orbr{\begin{cases}x=4\\x=6\end{cases}}\)
Vậy x = 4 hoặc x = 5 hoặc x = 6
\(a)\left(x-5\right)^{12}=\left(x-5\right)^{10}\)
\(\Leftrightarrow\left(x-5\right)^{12}-\left(x-5\right)^{10}=0\)
\(\Leftrightarrow\left(x-5\right)^{10}\left[\left(x-5\right)^2-1\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x-5\right)^{10}=0\\\left(x-5\right)^2-1=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-5=0\\\left(x-4\right)\left(x-6\right)=0\end{cases}}\)
[ ra \(\left(x-4\right)\left(x-6\right)\)do \(\left(x-5\right)^2-1=\left(x-5-1\right)\left(x-5+1\right)=\left(x-6\right)\left(x-4\right)\)]
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=4;x=6\end{cases}}\)
_Minh ngụy_
71-(33+x)=26
33+x=71-26
33+x=45
x=45-33
x=12
Vậy x=12
45-(x-9):2=6
(x-9):2=45-6
(x-9):2=39
x-9=39.2
x-9=78
x=78+9
x=87
Vậy x=87
\(77-\left(33+x\right)=26\\ \Rightarrow33+x=77-26=51\\ \Rightarrow x=51-33=18\\ 45-\left(x-9\right):2=6\\ \Rightarrow\left(x-9\right):2=45-6=39\\ \Rightarrow x-9=39\cdot2=78\\ \Rightarrow x=78+9=87\)
a)(x+35)-2.(-4)^2=-61
<=>x+35-32=-61
<=>x=-64
b)2^2.(-3)-(x+27)=-34
<=>-12-x-27=-34
<=>x=-5
c)3-3./x+4/=-27
<=>/x+4/=10
<=>x+4=10
x+4=-10
<=>x=6;-14
\(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{x.\left(x+2\right)}=\dfrac{4}{9}\)
=\(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{x}-\dfrac{1}{x-2}\)
=\(\dfrac{1}{2}-\dfrac{1}{x+2}\)=\(\dfrac{4}{9}\)
=>\(\dfrac{1}{x+2}=\dfrac{1}{2}-\dfrac{4}{9}=\dfrac{1}{18}\)
=>\(x+2=18\)
=>x=16
\(4^{x+2}+5.4^x=84\Rightarrow4^x\left(4^2+5\right)=84\Rightarrow4^x=4^1\Rightarrow x=1\)
\(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{x\left(x+2\right)}=\dfrac{4}{9}\)
\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{x}-\dfrac{1}{x+2}=\dfrac{4}{9}\)
\(\Rightarrow\dfrac{1}{2}-\dfrac{1}{x+2}=\dfrac{4}{9}\)
\(\Rightarrow\dfrac{x+2-2}{2\left(x+2\right)}=\dfrac{4}{9}\)
\(\Rightarrow\dfrac{x}{2x+4}=\dfrac{4}{9}\)
\(\Rightarrow9x=8x+16\)
\(\Rightarrow x=16\)
Vậy x = 16
Tìm x :
2/2.4 + 2/4.6 +....+ 2/x(x+2) = 4/9
=> 1/2 - 1/4 + 1/4 - 1/6 + ...+ 1/x - 1/(x + 2) = 4/9
=> 1/2 - 1/(x + 2) = 4/9
=> 1/(x + 2) = 1/18
=> x + 2 = 18
=> x = 16
ĐKXĐ: x ≠ 0; x ≠ -2
2/(2.4) + 2/(4.6) + ... + 2/[x(x + 2)] = 4/9
1/2 - 1/4 + 1/4 - 1/6 + ... + 1/x - 1/(x + 2) = 4/9
1/2 - 1/(x + 2) = 4/9
9(x + 2) - 18 = 4.2(x + 2)
9x + 18 - 18 = 8x + 16
9x - 8x = 16
x = 16 (nhận)
Vậy x = 16