Question

Tìm x:

2^x+2 - 3.2^x =16

\(\left(\frac{1}{5}-\frac{3}{2}x\right)^2=\frac{9}{4}\)

 

Answer 1

\(2^{x+2}-3.2^x=16\)

=> \(2^x.2^2-3.2^x=16\)

=> \(2^x.\left(2^2-3\right)=16\)

=> \(2^x.1=2^4\)

=> x = 4

\(\left(\frac{1}{5}-\frac{3}{2}x\right)^2=\frac{9}{4}\)

=> \(\left(\frac{1}{5}-\frac{3}{2}x\right)^2=\left(\frac{3}{2}\right)^2\)

=> \(\orbr{\begin{cases}\frac{1}{5}-\frac{3}{2}x=\frac{3}{2}\\\frac{1}{5}-\frac{3}{2}x=-\frac{3}{2}\end{cases}}\)

=> \(\orbr{\begin{cases}\frac{3}{2}x=\frac{1}{5}-\frac{3}{2}\\\frac{3}{2}x=\frac{1}{5}+\frac{3}{2}\end{cases}}\)

=> \(\orbr{\begin{cases}\frac{3}{2}x=-\frac{13}{10}\\\frac{3}{2}x=\frac{17}{10}\end{cases}}\)

=> \(\orbr{\begin{cases}x=\frac{-13}{15}\\x=\frac{17}{15}\end{cases}}\)