\(C=\left(1-2-3-4\right)+...+\left(197-198-199-200\right)\)

=-8x25=-200

\(D=-\left(11+13+...+99\right)+\left(10+12+...+98\right)\)

=(-1)+(-1)+...+(-1)

=-1x45=-45

bằng 10

\(A=x^5-5x^4+5x^3-5x^2+5x\)

\(=x^5-\left(x+1\right)x^4+\left(x+1\right)x^3-\left(x+1\right)x^2+\left(x+1\right)x\)

\(=x^5-x^5-x^4+x^4+x^3-x^3-x^2+x^2+x\)

\(=x\)

\(=4\)

b) Ta có: \(B=\sqrt{10-2\sqrt{21}}+\sqrt{10+2\sqrt{21}}\)

\(=\sqrt{7}-\sqrt{3}+\sqrt{7}+\sqrt{3}\)

\(=2\sqrt{7}\)

d) Ta có: \(D=\sqrt{x^2-6x+9}-x\)

\(=\left|x-3\right|-x\)

\(=\left[{}\begin{matrix}x-3-x=-3\left(x\ge3\right)\\3-x-x=-2x+3\left(x< 3\right)\end{matrix}\right.\)

A

Chọn A

A

\(a,Q=\left(A-B\right)\left(A+B\right)\\ b,ĐK:A,B\in R\)

B=x²y²+xy+x³+y³

Thay x=-1, y=3 ta có:

B=x²y²+xy+x³+y³

  =(-1)².3²+(-1).3+(-1)³+3³

  = 1.9-3-1+27

  = 9-3-1+27

  = 32

 giá trị biểu thức tại x = –1; y = 3 là:

\(B=\left(-1\right)^2.3^2+\left(-1\right).3+\left(-1\right)^3+3^3\\B=9-3-1+27\\ B=32 \)

Thay x=-1 và y=3 vào B, ta được:

\(B=\left(-1\right)^2\cdot3^2+\left(-1\right)\cdot3+\left(-1\right)^3+3^3=32\)

Ta có:

\(x^2-2018x+1=0\)

\(\Leftrightarrow x^2+1=2018x\)

Do đó

\(B=\frac{x^4+x^2+1}{x^2}=\frac{\left(x^4+2x^2+1\right)-x^2}{x^2}=\frac{\left(x^2+1\right)^2-x^2}{x^2}=\frac{\left(x^2+x+1\right)\left(x^2-x+1\right)}{x^2}\)

\(\Leftrightarrow B=\frac{\left(2018x+x\right)\left(2018x-x\right)}{x^2}=\frac{2019x\cdot2017x}{x^2}=2019\cdot2017\)