\(4\left(2x+1\right)^2=576\)

\(\left(2x+1\right)^2=\dfrac{576}{4}=144=12^2\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+1=12\\2x+1=-12\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=11\\2x=-13\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{11}{2}\\x=-\dfrac{13}{2}\end{matrix}\right.\)

\(4\cdot(2x+1)^2=576\\\Rightarrow (2x+1)^2=576:4\\\Rightarrow(2x+1)^2=144\\\Rightarrow(2x+1)^2=(\pm12)^2\)

\(\Rightarrow\left[{}\begin{matrix}2x+1=12\\2x+1=-12\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=11\\2x=-13\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{11}{2}\\x=-\dfrac{13}{2}\end{matrix}\right.\)

Vậy: \(x\in\left\{-\dfrac{13}{2};\dfrac{11}{2}\right\}\)

4.(2x+1)²=576

(2x+1)²   =576:4

(2x+1)²   =144

 144        =12² 

    (2x+1) =12

      2x      =12-1

      2x      =11

        x      =11:2

        x      =\(\dfrac{11}{2}\)

Vậy x = \(\dfrac{11}{2}\)

sửa đề :

2^x + 2^x+3 = 576

2^x . 1 + 2^x . 2³ = 576

2^x . ( 1 + 2³ ) = 576

2^x . 9 = 576

2^x = 576 : 9

2^x = 64

2^x = 2⁶

=> x = 6

2^x+2^x+3=576

2^x(1+2³)=576

2^x=579/9

2^x=64

2^x=2⁶

x=6

\(2^{3+x}+2^x=576\)

\(\Rightarrow2^x\cdot2^3+2^x=576\)

\(\Rightarrow2^x\cdot\left(2^3+1\right)=576\)

\(\Rightarrow2^x\cdot\left(8+1\right)=576\)

\(\Rightarrow2^x\cdot9=576\)

\(\Rightarrow2^x=576:9\)

\(\Rightarrow2^x=64\)

\(\Rightarrow2^x=2^6\)

\(\Rightarrow x=6\)

Vậy $x=6$.

\(2^{3+x}+2^x=576.\)

\(2^3.2^x+2^x.1=576\)

\(2^x.\left(2^3+1\right)=576\)

\(2^x.9=576\)

\(2^x=576:9\)

\(2^x=64\)

\(2^x=2^6\)

\(\Rightarrow x=6\)

ít thôi bạn à

tham khảo các câu trả lời của mình nhé

thống kê hỏi đáp

\(a) \frac{x}{2}=\frac{y}{-3}=\frac{z}{5}\) và \(2x+3y+5z=6\)

Ta có: \(\frac{x}{2}=\frac{y}{-3}=\frac{z}{5}=\frac{2x}{4}=\frac{3y}{-9}=\frac{5z}{25}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{2x}{4}=\frac{3y}{-9}=\frac{5z}{25}=\frac{2x+3y+5z}{4+(-9)+25}=\frac{6}{20}=\frac{3}{10}\)

Suy ra: +) \(\frac{x}{2}=\frac{3}{10}\implies x=\frac{3.2}{10}=\frac{3}{5}\)

            +) \(\frac{y}{-3}=\frac{3}{10}\implies y=\frac{3.(-3)}{10}=\frac{-9}{10}\)

            \(+) \frac{z}{5}=\frac{3}{10}\implies z=\frac{3.5}{10}=\frac{3}{2}\)

Vậy \(x=\frac{3}{5};y=\frac{-9}{10};z=\frac{3}{2}\)