Question

a) 3x -/2x+1/= 2

b) cho a/b=b/c=a/d . chứng minh ( a+b+c/b+c+d)^3

c) tính giá trị nhỏ nhất A = /x/+/8-x/

d) A= 1+ 3/2^3+4/2^4+5/2^5+...+100/2^100

e) tìm n thuộc Z sao cho : 2n -3 chia hết n+1

- giúp cái , còn chỗ này nữa.....

Answer 1

a: \(3x-\left|2x+1\right|=2\)

\(\Leftrightarrow\left|2x+1\right|=3x-2\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(3x-2\right)^2-\left(2x+1\right)^2=0\\x>=\dfrac{2}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(3x-2-2x-1\right)\left(3x-2+2x+1\right)=0\\x>=\dfrac{2}{3}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-3\right)\left(5x-1\right)=0\\x>=\dfrac{2}{3}\end{matrix}\right.\Leftrightarrow x=3\)

e: Ta có: \(2n-3⋮n+1\)

\(\Leftrightarrow2n+2-5⋮n+1\)

\(\Leftrightarrow n+1\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{0;-2;4;-6\right\}\)