cho a+b=2020. Tính S= -(-a+b+c)+(-c-b-a)-(a-b)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
S=-(-a+b+c)+(-c-b-a)-(a-b)
=a-b-c-c-b-a-a+b
=a+(-b)+(-c)+(-c)+(-b)+(-a)+(-a)+b
=[a+(-a)]+[(-b)+b]+[(-a)+(-b)]+[(-c)+(-c)]
=0+0+(-2020)+(-2c)
=-2020-2c
Vậy S=-2020-2c
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a^{2020}+b^{2020}+c^{2020}=a^{1010}b^{1010}+b^{1010}c^{1010}+c^{1010}a^{1010}\)
\(\Leftrightarrow a^{2020}+b^{2020}+c^{2020}-a^{1010}b^{1010}-b^{1010}c^{1010}-c^{1010}a^{1010}=0\)
\(\Leftrightarrow2a^{2020}+2b^{2020}+2c^{2020}-2a^{1010}b^{1010}-2b^{1010}c^{1010}-2a^{1010}c^{1010}=0\)
\(\Leftrightarrow\left(a^{2020}-2a^{1010}b^{1010}+b^{2020}\right)+\left(b^{2020}-2b^{1010}c^{1010}+c^{2020}\right)+\left(c^{2020}-2a^{1010}c^{1010}+a^{2020}\right)=0\)
\(\Leftrightarrow\left(a^{1010}-b^{1010}\right)^2+\left(b^{1010}-c^{1010}\right)^2+\left(c^{1010}-a^{1010}\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}\left(a^{1010}-b^{1010}\right)=0\\b^{1010}-c^{1010}=0\\c^{1010}-a^{1010}=0\end{cases}}\Leftrightarrow a^{1010}=b^{1010}=c^{1010}\Leftrightarrow\pm a=\pm b=\pm c\)
Rồi thay :> Còn thay kiểu nào thì mình cũng hong biết :">
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a^2+b^2+c^2=1\Rightarrow-1\le a,b,c\le1;a^3-a^2+b^3-b^2+c^3-c^2\)
\(=a^2\left(a-1\right)+b^2\left(b-1\right)+c^2\left(c-1\right)=0\Rightarrow a^2\left(a-1\right)=0;b^2\left(b-1\right)=0;c^2\left(c-1\right)=0\)
\(\text{kết hợp với:}a^3+b^3+c^3=1\Rightarrow\text{có 2 số bằng 0; 1 số bằng 1}\Rightarrow S=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
S = - a + b + c - c + b + a - a - b
S = - a
Vì a = 1 => S = -1
![](https://rs.olm.vn/images/avt/0.png?1311)
S=-(a-b-c)+(-c+b+a)-(a+b)
=-a+b+c-c+b+a-a-b
=-a+b+c+(-c)+b+a+(-a)+(-b)
=[(-a)+a+(-a)]+[b+b+(-b)]+[c+(-c)]
=-a+b
vì a>b nên |S|=a-b
vậy...
k mình nha. kb nữa...^_^...
S = -( -a + b + c ) + ( -c - b - a ) - ( a - b )
S = a - b - c - c - b - a - a + b
S = - a - b - 2c
\(S=-\left(-a+b+c\right)+\left(-c-b-a\right)-\left(a-b\right)\)
\(S=a-b-c-c-b-a-a+b\)
\(S=-2c-a-b\)
\(S=-2c-\left(a+b\right)\)
\(S=-2c-2020\)
hok tốt!!