Question

[dangthuylinh]

Bài 1:Tính và tìm x a) 1-2+3-4+5-6+..........+213-214

b)|x-17|+13=25

Answer 1

[Trần Đăng Nhất]

a) \(1-2+3-4+...+213-214\)

\(=\left(1-2\right)+\left(3-4\right)+...+\left(213-214\right)\)(có 107 cặp)

\(=\left(-1\right)+\left(-1\right)+...+\left(-1\right)\)

\(=-107\)

b) \(\left|x-17\right|+13=25\)

\(\Rightarrow\left|x-17\right|=25-13\)

\(\Rightarrow\left|x-17\right|=12\)

\(\Rightarrow\left[{}\begin{matrix}x-17=12\\17-x=12\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=12+17\\-x=12-17\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=29\\-x=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=29\\x=5\end{matrix}\right.\)

Vậy \(\left[{}\begin{matrix}x=29\\x=5\end{matrix}\right.\)

Answer 2

[Mashiro Shiina]

\(1-2+3-4+5-6+...+213-214\)

\(=\left(1-2\right)+\left(3-4\right)+\left(5-6\right)+...+\left(213-214\right)\)

\(=\left(-1\right)+\left(-1\right)+\left(-1\right)+...+\left(-1\right)\)

\(=\left(-1\right)\left[\left(\dfrac{214-1}{1}+1\right):2\right]\)

\(=-1.107\)

\(=-107\)

\(\left|x-17\right|+13=25\)

\(\Rightarrow\left|x-17\right|=12\)

\(\Rightarrow\left[{}\begin{matrix}x-17=12\\x-17=-12\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=29\\x=5\end{matrix}\right.\)