Question

tìm x biết:

a. 2*|x-1|-|1-x|=12

b. 2^x+2^x+3=144

Answer 1

a. \(2\left|x-1\right|-\left|1-x\right|=12\\ 2\left|x-1\right|-\left|x-1\right|=12\\ \left|x-1\right|\left(2-1\right)=12\\ \left|x-1\right|=12\\ \Rightarrow\left[{}\begin{matrix}x-1=12\\x-1=-12\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=13\\x=-11\end{matrix}\right.\)

Vậy \(x\in\left\{13;-11\right\}\)

b. \(2^x+2^{x+3}=144\\ 2^x\left(1+2^3\right)=144\\ 2^x.9=144\\ 2^x=144:9\\ 2^x=16\\ 2^x=2^4\\ \Rightarrow x=4\)

Vậy x = 4