\(4^x=64\\ 4^x=4^3\\ x=3\)

4^x = 64

4^x = 4³

x  = 3

a) \(\left(2x-3\right)^4=5^4\)

\(\Rightarrow\left[{}\begin{matrix}2x-3=5\\2x-3=-5\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=8\\2x=-2\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{8}{2}=4\\x=-\dfrac{2}{2}=-1\end{matrix}\right.\)

b) \(\left(2x-3\right)^3=-64\)

\(\Rightarrow\left(2x-3\right)^3=\left(-4\right)^3\)

\(\Rightarrow2x-3=-4\)

\(\Rightarrow2x=-1\)

\(\Rightarrow x=-\dfrac{1}{2}\)

a/

\(\left(2x-3\right)^4=5^4\\ \Leftrightarrow\left|2x-3\right|=5\\ \Leftrightarrow\left[{}\begin{matrix}2x-3=5\\2x-3=-5\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x=8\\2x=-2\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=4\\x=-1\end{matrix}\right.\)

Vậy...

b/ 2x-3=-64

<=>2x = -61

<=> x = -61/2

câu 1= 13288

câu 2= 14368

câu 1= 13288

câu 2=14368

chúc bạn học giỏi

\(\Leftrightarrow36\left(x+6\right)+36\left(x-6\right)=\dfrac{9}{2}\left(x^2-36\right)\)

\(\Leftrightarrow x^2\cdot\dfrac{9}{2}-162-72x=0\)

\(\Leftrightarrow9x^2-144x-324=0\)

\(\Leftrightarrow x^2-16x-36=0\)

=>(x-18)(x+2)=0

=>x=18 hoặc x=-2

ĐKXĐ:\(x\ne\pm6\)

\(\dfrac{36}{x-6}+\dfrac{36}{x+6}=4,5\\ \Leftrightarrow36\left(\dfrac{1}{x-6}+\dfrac{1}{x+6}\right)=4,5\\ \Leftrightarrow\dfrac{x+6}{\left(x-6\right)\left(x+6\right)}+\dfrac{x-6}{\left(x-6\right)\left(x+6\right)}=\dfrac{1}{8}\\ \Leftrightarrow\dfrac{x+6+x-6}{x^2-36}=\dfrac{1}{8}\\ \Leftrightarrow\dfrac{2x}{x^2-36}=\dfrac{1}{8}\\ \Leftrightarrow x^2-36=16x\\ \Leftrightarrow x^2-16x-36=0\\ \Leftrightarrow\left(x^2+2x\right)-\left(18x+36\right)=0\\ \Leftrightarrow x\left(x+2\right)-18\left(x+2\right)=0\\ \Leftrightarrow\left(x+2\right)\left(x-18\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\left(tm\right)\\x=18\left(tm\right)\end{matrix}\right.\)

\(\dfrac{36}{x+6}+\dfrac{36}{x-6}=4,5\)

\(\Leftrightarrow36\left(x-6\right)+36\left(x+6\right)=4,5\left(x^2-36\right)\)

\(\Leftrightarrow36x-216+36x+216=4,5x^2-162\)

\(\Leftrightarrow-4,5x^2+72x+162=0\)

\(\Leftrightarrow\left(x-18\right)\left(-4,5x-9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=18\\x=-2\end{matrix}\right.\)

1C

2A

1C        2A

=9( 1/4.5+1/5.6+...+1/36.37)

=9( 1/4-1/37)... tự yinhs nha

\(\frac{36}{x+6}+\frac{36}{x-6}=\) \(4,5\)\(\left(ĐKCĐ:x\ne\pm6\right)\)

\(\Leftrightarrow\frac{36\left(x-6\right)}{\left(x+6\right)\left(x-6\right)}+\frac{36\left(x+6\right)}{\left(x+6\right)\left(x-6\right)}\)\(=\frac{4,5\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}\)

\(\Leftrightarrow\frac{36x-216}{\left(x-6\right)\left(x+6\right)}+\frac{36x+216}{\left(x-6\right)\left(x+6\right)}\)\(=\frac{4,5x^2-162}{\left(x-6\right)\left(x+6\right)}\)

\(\Rightarrow36x-216+36x+216=4,5x^2-162\)

( đến đây giải phương trình ra rồi đối chiếu đkxđ là xong )

\(\frac{36}{x+6}+\frac{36}{x-6}=4,5\)

\(\frac{36}{x+6}+\frac{36}{x-6}=\frac{4,5\left(x+6\right)\left(x-6\right)}{\left(x+6\right)\left(x-6\right)}\)

\(DKXD:\hept{\begin{cases}x+6\ne0\\x-6\ne0\\\left(x+6\right)\left(x-6\right)\ne0\end{cases}}\Leftrightarrow\hept{\begin{cases}x\ne-6\\x\ne6\end{cases}}\)

\(\frac{72x}{\left(x+6\right)\left(x-6\right)}=\frac{4,5\left(x+6\right)\left(x-6\right)}{\left(x+6\right)\left(x-6\right)}\)

\(4,5x^2+72x-162=0\)

\(4,5x^2-9x+81x-162=0\)

\(4,5\left(x-2\right)+81\left(x-2\right)=0\)

\(\left(x-2\right)\left(4,5x-81\right)=0\)

\(\left(x-2\right)4,5\left(x-18\right)=0\)

\(\hept{\begin{cases}x-2=0\\x-18=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=2\\x=18\end{cases}}\)

Ta có:\(\left(\frac{6}{x^2-6x}+\frac{1}{x+6}\right):\frac{x^2+36}{x^2-36}\)

   \(=\left(\frac{6\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)}+\frac{x\left(x-6\right)}{x\left(x-6\right)\left(x+6\right)}\right).\frac{x^2-6^2}{x^2+36}\)

     \(=\left(\frac{6x+36+x^2-6x}{x\left(x-6\right)\left(x+6\right)}\right).\frac{\left(x-6\right)\left(x+6\right)}{x^2+36}\)

        \(=\frac{x^2+36}{x\left(x-6\right)\left(x+6\right)}.\frac{\left(x-6\right)\left(x+6\right)}{x^2+36}\)

      \(=\frac{1}{x}\)

Kiểm tra đi bạn phải là \(\frac{1}{x}\)