Câu hỏi của Vương Hàn

Question

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

b ) Tìm x biết : | x ( x - 4 ) | = x

Truy kích · Accepted Answer

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)

Câu trả lời:

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)

Nguyễn Huy Tú · Answer

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