tìm x biết |x- 1/2| + 2/3 = |1/3 - 2,5|
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![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(x^2+2x=y^2\\ \Leftrightarrow x^2+2x+1=y^2+1\\ \Leftrightarrow\left(x+1\right)^2-y^2=1\\ \Leftrightarrow\left(x+1-y\right)\left(x+1+y\right)=1=1.1\)
Vì x,y nguyên nên x+1-y và x+1+y nguyên.
Do đó: \(\left\{{}\begin{matrix}x+1-y=1\\x+1+y=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x+y=0\\x-y=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=0\\y=0\end{matrix}\right.\)
Cặp số nguyên (x,y) thõa mãn bài toán là (0;0)
![](https://rs.olm.vn/images/avt/0.png?1311)
( 10 - \(\dfrac{5}{3}\) + \(\dfrac{4}{9}\)) - ( 7- \(\dfrac{8}{3}\)- \(\dfrac{4}{9}\))
= 10 - \(\dfrac{5}{3}\) + \(\dfrac{4}{9}\) - 7 + \(\dfrac{8}{3}\) + \(\dfrac{4}{9}\)
= ( 10 - 7) + ( \(\dfrac{8}{3}\)- \(\dfrac{5}{3}\)) + ( \(\dfrac{4}{9}\) + \(\dfrac{4}{9}\))
= 3 + \(\dfrac{3}{3}\) + \(\dfrac{8}{9}\)
= 4 + \(\dfrac{8}{9}\)
= \(\dfrac{36}{9}\) + \(\dfrac{8}{9}\)
= \(\dfrac{44}{9}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
TH1: \(3-2x\ge0\Leftrightarrow x\le\dfrac{3}{2}\)
\(\Rightarrow\left(2x-3\right)^2=3-2x\)
\(\Leftrightarrow\left(2x-3\right)^2+2x-3=0\)
\(\Leftrightarrow\left(2x-3\right)\left(2x-3+1\right)=0\)
Giải nhanh: \(x=\dfrac{3}{2}\)(nhận) hay \(x=1\) (nhận)
TH2: \(3-2x< 0\Leftrightarrow x>\dfrac{3}{2}\)
\(\Rightarrow\left(2x-3\right)^2=2x-3\)
Giải tương tự, ta suy ra \(x=\dfrac{3}{2}\) (loại) hay \(x=2\) (nhận)
Kết luận phương trình có 3 nghiệm \(x=1;x=\dfrac{3}{2};x=2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{3}{5}.\dfrac{5}{7}+\dfrac{3}{5}:\dfrac{5}{3}-\dfrac{1}{7}:\dfrac{5}{3}\)
= \(\dfrac{3}{5}.\dfrac{5}{7}-\dfrac{3}{7}.\dfrac{3}{5}-\dfrac{1}{7}.\dfrac{3}{5}\)
=\(\dfrac{3}{5}.\left(\dfrac{5}{7}+\dfrac{3}{7}-\dfrac{1}{7}\right)\)
=\(\dfrac{3}{5}.1\)
=\(\dfrac{3}{5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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`500 - {5.[409 - (2^3 . 3 - 21)^3 ] - 1724}`
`=500 - {5.[409 - (8.3-21)^3 ] - 1724}`
`=500- {5 . [409 - (24-21)^3 ] - 1724}`
`=500 - {5 .[409 - 3^3] - 1724}`
`=500 - {5.382 - 1724}`
`=500 - {1910 - 1724}`
`=500 - 186`
`=314`
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`375 : { 32 - [4 + ( 5.3^2 - 42)]} -14`
`=375 :{ 32 - [4 + ( 5 . 9 - 42)]} -14`
`=375 : { 32 - [4 + (45-42)]}-14`
`=375 :{32-[4+3]}-14`
`=375 : 25-14`
`=15-14`
`=1`
|x- 1/2| +2/3 = | 1/3 -2,5|
|x-1/2| + 2/3 = |-13/6|
| x -1/2| + 2/3 = 13/6
| x-1/2| = 13/6 - 2/3
|x-1/2| = 3/2
x - 1/2 = + - 3/2
x = 2; x = - 1
vậy x ϵ {-1; 2}