1+1 div 2 + 1 div 3 + 1 div 4
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
Đặt \(t=2x^2+3x-1\) ta có:
\(t^2-5\left(t+4\right)+24=0\)
\(\Rightarrow t^2-5t-20+24=0\)
\(\Rightarrow t^2-5t+4=0\)
\(\Rightarrow\left(t-4\right)\left(t-1\right)=0\)\(\Rightarrow\left[\begin{matrix}t=4\\t=1\end{matrix}\right.\)
*)Xét \(2x^2+3x-1=4\)
\(\Rightarrow\left(x-1\right)\left(2x+5\right)=0\)\(\Rightarrow\left[\begin{matrix}x=1\\x=-\frac{5}{2}\end{matrix}\right.\)
*)Xét \(2x^2+3x-1=1\)
\(\Rightarrow\left(x+2\right)\left(2x-1\right)=0\)\(\Rightarrow\left[\begin{matrix}x=-2\\x=\frac{1}{2}\end{matrix}\right.\)
Bài 2:
\(\left(x^2-4\right)\left(x+3\right)=\left(x^2-4\right)\left(x-1\right)\)
\(\Rightarrow\left(x^2-4\right)\left(x+3\right)-\left(x^2-4\right)\left(x-1\right)=0\)
\(\Rightarrow\left(x^2-4\right)\left[x+3-\left(x-1\right)\right]=0\)
\(\Rightarrow4\left(x-2\right)\left(x+2\right)=0\)
\(\Rightarrow\left(x-2\right)\left(x+2\right)=0\)\(\Rightarrow\left[\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}+1\right)\cdot\cdot\cdot\left(\dfrac{1}{99}+1\right)=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{100}{99}=\dfrac{3\cdot4\cdot....\cdot100}{2\cdot3\cdot...\cdot99}=\dfrac{100}{2}=50\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) 2a - 1, b + 3, 5 - 2c TLT với 2 , 3 , 4
=>\(\frac{2a-1}{2}=\frac{b+3}{3}=\frac{5-2c}{4}=k\left(kthuocZ\right)\)
=>a=2k+1,b=3k-3,c=(5-4k)/2
Thay vao a+b-c=2 tim duoc k, chu y k thuoc Z, tu do suy ra a,b,c.
b) Tuong tu.
![](https://rs.olm.vn/images/avt/0.png?1311)
1) 167 + ( -252 ) + 52 + ( -67 )
= 167 + 52 + ( -252 ) + ( - 67 )
= 219 + - ( 252 + 67 )
= 219 + - ( 319 )
= -100
2) ( -215 ) + ( - 115 ) + ( - 80 )
= - ( 215 + 115 ) + ( - 80 )
= - 330 + ( - 80 )
= - ( 330 - 80 )
= - 250
3) 118 + 107 - ( 118 - 93 )
= 118 + ( 107 - 93 )
= 118 + 14
= 132
4) 1 + 5 + 9 + ..... + 97 + 101
= ( 101 : 1) - 4 = 96
= 101 x 96
= 9696
5) 38 - 138 + 250 - 350
= - 100 + - 100
= 0
6) - ( - 357 ) + ( - 27 ) + ( - 32 )
= - ( - 357 ) + - ( 27 + 32 )
= - ( - 357 ) + - 59
= - ( 357 + 59 )
= - 416
7) 40 + ( 139 - 172 + 99 ) - ( 139 + 199 - 172 )
= 40 + ( 100 - 100 )
= 40 + 0
= 40
8) ( -1 ) + 2 + ( - 3 ) + 4 + ( - 99 ) + 100
![](https://rs.olm.vn/images/avt/0.png?1311)
1+1 div 2+1 div 3+1 div 4
=1+0+0+0
=1