Question

a, \(2^x+2^{x+1}+2^{x+2}=112\)

b,\(|x+\frac{1}{1.2}|+|x+\frac{1}{2.3}|+|x+\frac{1}{3.4}|+...+|x+\frac{1}{99.100}|=100x\)

Answer 1

a) \(2^x+2^{x+1}2^{x+2}=112\)

    \(2^x.\left(1+2+4\right)=112\)

     \(2^x=112:7=16\)

Mà \(2^4=16\)

\(\Rightarrow2^x=2^4\)

Vậy x = 4

b) \(\left|x+\frac{1}{1.2}\right|+\left|x+\frac{1}{2.3}\right|+...\left|x+\frac{1}{99.100}\right|=100x\)

Vì \(\left|x+\frac{1}{1.2}\right|\ge0;\left|x+\frac{1}{2.3}\right|\ge0;....\left|x+\frac{1}{99.100}\right|\ge0\)

\(\Rightarrow\left(x+x+...x\right)+\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\right)=100x\)

\(\Rightarrow100x+\left(1-\frac{1}{100}\right)=100x\)

\(\Rightarrow\frac{99}{100}=x\)

Answer 2

a) 2^x+2^x+1+2^x+2=112

  2^x(1+2+2²)=112

2^x.7=12

2^x=16

x=4