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![](https://rs.olm.vn/images/avt/0.png?1311)
(a-b-c)-(c+b-a)= -1
<=>a-b-c-c-b-a= -1
<=> -2b-2c= -1
=> 2010a+2009=0+2009=2009
b) Số nguyên thỏa mãn là 0
![](https://rs.olm.vn/images/avt/0.png?1311)
\(40^2-39^2+38^2-37 ^2+...+2^2-1^2\)
= \(\left(40+39\right)\left(40-39\right)+\left(38+37\right)\left(38-37\right)+....+\left(2+1\right)\left(2-1\right)\)
= \(79.1+75.1+....+3.1\)
= \(79+75+....+3\)
= \(\left(79+3\right)\left[\left(79-3\right):4+1\right]:2\)
= \(82.20:2\)
= \(820\)
\(\left(3x-1\right)^2+2\left(x+3\right)^2+11\left(x+1\right)\left(1-x\right)=6\)
=> \(9x^2-6x+1+2x^2+12x+18-11x^2+11=6\)
=> \(6x+30=6\)
=> \(6x=6-30\)
=> \(6x=-24\)
=> \(x=-24:6=-4\)
\(\text{a) }40^2-39^2+38^2-37^2+...+2^2-1^2\)
\(=\left(40^2-39^2\right)+\left(38^2-37^2\right)+...+\left(2^2-1^2\right)\)
\(=\left(40-39\right)\left(40+39\right)+\left(38-37\right)\left(38+37\right)+...+\left(2-1\right)\left(2+1\right)\)
\(=1.79+1.75+...+1.3\)
\(=79+75+...+3\)
\(\text{Từ 3 đến 79 có: (79 - 3) : 2 + 1 = 39 (số hạng)}\)
\(\text{Tổng là: }\frac{\left(79+3\right)\times39}{2}=1599\)
\(\text{b) }\left(3x-1\right)^2+2\left(x+3\right)^2+11\left(x+1\right)\left(1-x\right)=6\)
\(\Leftrightarrow\left(9x^2-6x+1\right)+2\left(x^2+6x+9\right)+11\left(1-x^2\right)=6\)
\(\Leftrightarrow9x^2-6x+1+2x^2+12x+18+11-11x^2=6\)
\(\Leftrightarrow\left(9x^2+2x^2-11x^2\right)+\left(-6x+12x\right)+\left(1+18+11\right)=6\)
\(\Leftrightarrow6x+30=6\)
\(\Leftrightarrow6x=6-30\)
\(\Leftrightarrow6x=-24\)
\(\Leftrightarrow x=-4\)
2014^5 - 2015. 2014^4 + 2015.2014^3 - 2015.2014^2 + 2015.2014 + 1
Tính nhanh không sử dụng máy tính ạ
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1) \(\left(3x-1\right)\left(2x+7\right)-\left(12x^3+8x^2-14x\right):2x\)
\(=6x^2+19x-7-6x^2-4x+7=15x\)
2) \(\left(63^3-37^3\right):26+63.37\)
\(=\left(63-37\right)\left(63^2+63.37+37^2\right):26+63.37\)
\(\left[26\left(63^2+63.37+37^2\right)\right]:26+63.37\)
\(63^2+2.63.37+37^2=\left(63+37\right)^2=100^2=10000\)
bằng 0