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a ) 13/20
B)
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\(=\frac{1}{3}+\frac{1}{15}+\frac{3}{5}-\left(\frac{3}{4}+\frac{2}{9}+\frac{1}{36}\right)+\frac{1}{64}=\frac{5+1+9}{15}-\frac{27+8+1}{36}+\frac{1}{64}.\)
\(=\frac{1}{64}\)
Đặt \(A=1+3^2+3^4+...+3^{100}\)
\(9A=3^2+3^4+3^6+...+3^{102}\)
\(9A-A=\left(3^2+3^4+3^6+...+3^{102}\right)-\left(1+3^2+3^4+...+3^{100}\right)\)
\(8A=3^{102}-1\)
\(A=\frac{3^{102}-1}{8}\)
Vậy \(A=\frac{3^{102}-1}{8}\)
Chúc bạn học tốt ~
Đặt A = 1 + 3^2 + 3^4 + 3^6 + ....+ 3^100
3^2A = 3^2 + 3^4 + 3^6 + ..+3^102
8A=3^2A - A = 3102 - 1
A = 3102 - 1/8
=. A = 3102 - 1 /8
\(x^{64}=x\)
\(\Rightarrow\hept{\begin{cases}x=0\\x=1\end{cases}}\)
vậy \(\hept{\begin{cases}x=0\\x=1\end{cases}}\)
\(\left(x-1\right)^4=9\left(x-1\right)^2\)
\(\left(x-1\right)^4-9\left(x-1\right)^2=0\)
\(\left(x-1\right)^2.\left[\left(x-1\right)^2-3^2\right]=0\)
\(\left(x-1\right)^2.\left(x-1-3\right)\left(x-1+3\right)=0\)
\(\left(x-1\right)^2.\left(x-4\right)\left(x-2\right)=0\)
\(\Rightarrow\left(x-1\right)^2=0\)hoặc \(\orbr{\begin{cases}x-4=0\\x-2=0\end{cases}}\)
\(\Rightarrow x-1=0\)hoặc \(\orbr{\begin{cases}x=4\\x=2\end{cases}}\)
vậy \(x=1\)hoặc \(\orbr{\begin{cases}x=4\\x=2\end{cases}}\)
Đặt \(A=1+2+2^2+2^3+...+2^{64}\)
\(\Rightarrow2A=2+2^2+2^3+...+2^{65}\)
\(\Rightarrow2A-A=2+2^2+2^3+...+2^{65}-\left(1+2+2^2+...+2^{64}\right)\)
\(\Rightarrow A=2+2^2+2^3+...+2^{65}-1-2-2^2-...-2^{64}\)
\(\Rightarrow A=2^{65}-1\)
Ta có :
\(\left(\frac{3}{4}x-\frac{1}{2}\right)^2-\frac{1}{64}=0\)
\(\Leftrightarrow\)\(\left(\frac{3}{4}x-\frac{1}{2}\right)^2=\frac{1}{64}\)
\(\Leftrightarrow\)\(\left(\frac{3}{4}x-\frac{1}{2}\right)^2=\frac{1^2}{8^2}\)
\(\Leftrightarrow\)\(\left(\frac{3}{4}x-\frac{1}{2}\right)^2=\left(\frac{1}{8}\right)^2\)
\(\Leftrightarrow\)\(\frac{3}{4}x-\frac{1}{2}=\frac{1}{8}\)
\(\Leftrightarrow\)\(\frac{3}{4}x=\frac{1}{8}+\frac{1}{2}\)
\(\Leftrightarrow\)\(\frac{3}{4}x=\frac{5}{8}\)
\(\Leftrightarrow\)\(x=\frac{5}{8}:\frac{3}{4}\)
\(\Leftrightarrow\)\(x=\frac{5}{8}.\frac{4}{3}\)
\(\Leftrightarrow\)\(x=\frac{5}{2}.\frac{1}{3}\)
\(\Leftrightarrow\)\(x=\frac{5}{6}\)
Vậy \(x=\frac{5}{6}\)
Chúc bạn học tốt ~
\(\left(\frac{3}{4}.x-\frac{1}{2}\right)^2-\frac{1}{64}=0\)
\(\left(\frac{3}{4}.x-\frac{1}{2}\right)^2=0+\frac{1}{64}=\frac{1}{64}\)
\(\left(\frac{3}{4}.x-\frac{1}{2}\right)^2=\left(\frac{1}{8}\right)^2\)
=>\(\frac{3}{4}.x-\frac{1}{2}=\frac{1}{8}\)
\(\frac{3}{4}.x=\frac{1}{8}+\frac{1}{2}\)
\(\frac{3}{4}.x=\frac{5}{8}\)
\(x=\frac{5}{8}:\frac{3}{4}\)
\(x=\frac{5}{6}\)