Question

1. Tìm x

\(3x.(2x-3/5) =0\)

2. Tính giá trị biểu thức

a/ Tìm giá trị lớn nhất của \(A=2,5-|1, 7-x|\)

b/ Cho a, b ∈ Z, b>0. So sánh hai số hữu tỉ a/b và a+2019/b+2019

Answer 1

1. Tìm x

\(3x.\left(2x-\frac{3}{5}\right)=0\)

⇒ \(\left[{}\begin{matrix}3x=0\\2x-\frac{3}{5}=0\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}x=0:3\\2x=0+\frac{3}{5}=\frac{3}{5}\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}x=0\\x=\frac{3}{5}:2\end{matrix}\right.\)

⇒ \(\left[{}\begin{matrix}x=0\\x=\frac{3}{10}\end{matrix}\right.\)

Vậy \(x\in\left\{0;\frac{3}{10}\right\}.\)

2.

b)

TH1: \(a< b.\)

\(\Rightarrow2019a< 2019b\)

\(\Rightarrow ab+2019a< ab+2019b.\)

\(\Rightarrow a.\left(b+2019\right)< b.\left(a+2019\right)\)

\(\Rightarrow\frac{a}{b}< \frac{a+2019}{b+2019}.\)

TH2: \(a=b.\)

\(\Rightarrow\frac{a}{b}=\frac{a+2019}{b+2019}.\)

TH3: \(a>b.\)

\(\Rightarrow2019a>2019b.\)

\(\Rightarrow ab+2019a>ab+2019b\)

\(\Rightarrow a.\left(b+2019\right)>b.\left(a+2019\right).\)

\(\Rightarrow\frac{a}{b}>\frac{a+2019}{b+2019}.\)

Chúc bạn học tốt!

Answer 2

1

x . (2x - 3/ 5 ) = 0 : 3

2x - 3/ 5 = 0

2x = 0+3/5

x =3/ 5 : 2

x = 3/ 10