Question

a ) Tính A = 2²⁰¹⁷ - ( 2²⁰¹⁶ + 2²⁰¹⁵ + ... + 2¹ + 2⁰ )

b ) Tìm x biết : | x ( x - 4 ) | = x

Answer 1

a)Đặt \(A=2^{2016}+2^{2015}+...+2^1+2^0\)

\(2A=2\left(1+2+...+2^{2016}\right)\)

\(2A=2+2^2+...+2^{2017}\)

\(2A-A=\left(2+2^2+...+2^{2017}\right)-\left(1+2+...+2^{2016}\right)\)

\(A=2^{2017}-1\) thay vào ta có:

\(A=2^{2017}-\left(2^{2017}-1\right)=2^{2017}-2^{2017}+1=1\)

b)Ta thấy: \(\left|x\left(x-4\right)\right|\ge0\Rightarrow VT\ge0\Rightarrow VP\ge0\Rightarrow x\ge0\)

Ta có: \(x\left|x-4\right|=x\left(x\ge0\right)\)

Nếu x=0 thì 0|0-4|=0 (đúng)Nếu x\(\ne\)0 thì ta có \(\left|x-4\right|=1\Leftrightarrow x-4=\pm1\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=5\\x=3\end{array}\right.\)

Vậy x=0;x=5;x=3 (thỏa mãn)

 

 

 

 

Answer 2

a) Đặt \(B=2^{2016}+2^{2015}+...+2^1+2^0\)

\(\Rightarrow B=1+2+...+2^{2015}+2^{2016}\)

\(\Rightarrow2B=2+2^2+...+2^{2016}+2^{2017}\)

\(\Rightarrow2B-B=\left(2+2^2+...+2^{2016}+2^{2017}\right)-\left(1+2+...+2^{2015}+2^{2016}\right)\)

\(\Rightarrow B=2^{2017}-1\)

Mà \(A=2^{2017}-B\)

\(\Rightarrow A=2^{2017}-\left(2^{2017}-1\right)\)

\(\Rightarrow A=1\)

Vậy A = 1