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Bài 1 :
(x-4)2= (x-4)4
=> (x-4)2 - (x-4)4 = 0
=>(x-4)2 . [ 1 -(x-4)2 ] =0
=> \(\left[{}\begin{matrix}\left(x-4\right)^2=0\\1-\left(x-4\right)^2=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x-4=0\\\left[{}\begin{matrix}\left(x-4\right)=1\\x-4=-1\end{matrix}\right.\end{matrix}\right.\)
Sau đó tự tính nhé
Chúc bạn học tốt !
1/4×2/6×3/8×4/10×...×14/30×15/32=1/2^x
<=>1/(2×2)×2/(2×3)×...×14/(2×15)×15/2^5=1/2^x
<=>1/2×1/2×...×1/2×1/(2^5)=1/2^x
<=>1/2^19=1/2^x=>x=19
Đề mình không ghi lại nhé.
\(\Rightarrow\frac{1\times2\times3\times4\times...\times14\times15}{4\times6\times10\times...\times30\times32}=\frac{1}{2^x}\)\(\frac{1}{2^x}\)
\(\Rightarrow\frac{1\times2\times3\times4\times...\times14\times15}{2\times4\times6\times8\times10\times...\times30\times32}\)\(=\frac{1}{2^{x+1}}\)
\(\Rightarrow\frac{1}{2^{15}\times32}=\)\(\frac{1}{2^{x+1}}\)
\(\Rightarrow2^{15}\times2^5=2^{x+1}\)
\(\Rightarrow2^{20}=2^{x+1}\)
\(\Rightarrow x+1=20\Rightarrow x=19\)
Vậy \(x=1\)
Học tốt nhaaa!
Bài 1:
b) Ta có: \(D=\dfrac{-5}{10}\cdot\dfrac{-4}{10}\cdot\dfrac{-3}{10}\cdot...\cdot\dfrac{3}{10}\cdot\dfrac{4}{10}\cdot\dfrac{5}{10}\)
\(=\dfrac{-5}{10}\cdot\dfrac{-4}{10}\cdot\dfrac{-3}{10}\cdot...\cdot0\cdot...\cdot\dfrac{3}{10}\cdot\dfrac{4}{10}\cdot\dfrac{5}{10}\)
=0
Đặt \(A=2.2^2+3.2^3+4.2^4+5.2^5+...+n.2^n\)
\(\Rightarrow2A=2.2^3+3.2^4+4.2^5+5.2^6+...+n.2^{n+1}\)
\(\Rightarrow2A-A=2.2^3+3.2^4+4.2^5+5.2^6+...+n.2^{n+1}\)
\(-2.2^2-3.2^3-4.2^4-5.2^5-...-n.2^n\)
\(A=n.2^{n+1}-2^3-\left(2^3+2^4+...+2^n\right)\)
Đặt \(M=\left(2^3+2^4+...+2^n\right)\)
\(\Rightarrow2M=\left(2^4+2^5+...+2^{n+1}\right)\)
\(\Rightarrow M=2^{n+1}-2^3\)
\(\Rightarrow A=n.2^{n+1}-2^3-2^{n+1}+2^3\)
\(\Rightarrow A=\left(n-1\right)2^{n+1}=2^{n+10}\)
\(\Rightarrow\left(n-1\right)=2^9\)
\(\Rightarrow n=513\)
Đặt \(A=2.2^2+3.2^3+4.2^4+...+n.2^n=2^{n+10}\)
\(\Rightarrow2A=2.2^3+3.2^4+4.2^5+...+n.2^{n+1}\)
\(\Rightarrow2A-A=2.2^3+3.2^4+4.2^5+...+n.2^{n+1}-2.2^2-3.2^3-4.2^4-...-n.2^n\)
\(\Leftrightarrow A=-2.2^2+\left(2.2^3-3.2^3\right)+\left(3.2^4-4.2^4\right)+...+[\left(n-1\right)2^n-n.2^n]+n.2^{n+1}\)
\(\Leftrightarrow A=-2.2^2-2^3-2^4-...-2^n+n.2^{n+1}\)
\(\Leftrightarrow A=-2^3-\left(2^4-2^3\right)-\left(2^5-2^4\right)-...-\left(2^{n+1}-2^n\right)+n.2^{n+1}\)
\(\Leftrightarrow A=-2^3-2^4+2^3-2^5+2^4-...-2^{n+1}+2^n+n.2^{n+1}\)
\(\Leftrightarrow A=-2^{n+1}+n.2^{n+1}\)
\(\Leftrightarrow A=2^{n+1}\left(n-1\right)\)
Mà \(A=2^{n+10}=2^{n+1}.2^9=2^{n+1}.512\)
\(\Rightarrow n-1=512\)
\(\Rightarrow n=513\)
\(a,\frac{x+8}{3}+\frac{x+7}{2}=-\frac{x}{5}\)
\(\Leftrightarrow\frac{10\cdot\left(x+8\right)}{30}+\frac{15\left(x+7\right)}{30}=\frac{-6x}{30}\)
\(\rightarrow10x+80+15x+105=-6x\)
\(\Leftrightarrow31x+185=0\)
\(\Leftrightarrow x=-\frac{185}{31}\)
b,\(b,\frac{x-8}{3}+\frac{x-7}{4}=4+\frac{1-x}{5}\)
\(\Leftrightarrow\frac{20\left(x-8\right)}{60}+\frac{15\left(x-7\right)}{60}=\frac{240}{60}+\frac{12\left(1-x\right)}{60}\)
\(\rightarrow20x-160+15x-105=240+12-12x\)
\(\Leftrightarrow47x-517=0\)\(\Leftrightarrow x=11\)
