1,\(B=-x^2+20x-1=-\left(x^2-20x+1\right)\)

\(=-\left(x^2-2.10x+100-99\right)=-\left(x-10\right)^2+99\le99\)

Dấu ''='' xảy ra khi x = 10 

Vậy GTLN B là 99 khi x = 10 

2, \(E=x^2+2x\left(y+1\right)+y^2+2y+1\)

\(2E=2x^2+4x\left(y+1\right)+2y^2+4y+2\)

\(=2x^2+4xy+4x+2y^2+4y+2\)

\(=x^2+4xy+4y^2+x^2+4x+4-2\left(y^2-2y+1\right)\)
\(=\left(x+2y\right)^2+\left(x+2\right)^2-2\left(y-1\right)^2\ge0\)

Dấu ''='' xảy ra khi x = -2 ; y = 1 

Vậy GTNN E là 0 khi x = -2 ; y = 1 

\(a,x^2-9=0\)

\(x^2=9\)

\(\orbr{\begin{cases}x=\sqrt{9}\\x=-\sqrt{9}\end{cases}\orbr{\begin{cases}x=3\\x=-3\end{cases}}}\)

\(b,4x^2-4=0\)

\(x^2=1\)

\(\orbr{\begin{cases}x=\sqrt{1}\\x=-\sqrt{1}\end{cases}\orbr{\begin{cases}x=1\\x=-1\end{cases}}}\)

\(VT=3\left(x^2+y^2+z^2\right)-\left(x-y\right)^2-\left(y-z\right)^2-\left(z-x\right)^2=\left(x+y+z\right)^2\)

\(\Leftrightarrow3x^2+3y^2+3z^2-x^2+2xy-y^2-y^2+2yz-z^2-z^2+2xz-x^2=\left(x+y+z\right)^2\)

\(\Leftrightarrow x^2+y^2+z^2+2xy+2yz+2xz=\left(x+y+z\right)^2\)* luôn đúng *

Vậ ta có đpcm 

a, \(\left(2x+1\right)^2-\left(x-1\right)^2=0\)

\(\Leftrightarrow\left(2x+1-x+1\right)\left(2x+1+x-1\right)=0\)

\(\Leftrightarrow3x\left(x+2\right)=0\Leftrightarrow x=0;x=-2\)

b, \(\left(3x-1\right)^2-\left(x+5\right)^2=0\)

\(\Leftrightarrow\left(3x-1-x-5\right)\left(3x-1+x+5\right)=0\)

\(\Leftrightarrow\left(2x-6\right)\left(4x+4\right)=0\Leftrightarrow x=3;x=-2\)

a/ xét 2 tam giác AMB và CMK có:

AM = MC (M là t/đ AC)

góc KMC = góc BMA (đối đỉnh)

MK = MB (gt)

=> tam giác AMB = tam giác CMK (c.g.c)

=> góc MAB =  góc MCK = 90 độ hay KC vuông AC (đpcm)

b. xét hai tam giác AMK và CMB có:

AM = MC (M là t/đ AC)

góc AMK = góc CMB (đối đỉnh)

MK = MB (gt)

=> tg AMK = tg CMB (c.g.c)

=> góc AKM = góc CBM mà hai góc này ở vị trí sole trong nên AK // BC (đpcm)

g, sửa đề 

 \(5x^2-5xy+7y-7x=5x\left(x-y\right)+7\left(y-x\right)=\left(5x-7\right)\left(x-y\right)\)

h, sửa đề

 \(xy-xz+z-y=x\left(y-z\right)-\left(y-z\right)=\left(x-1\right)\left(y-z\right)\)

i, \(x^3+2x^2-3x-6=x^2\left(x+2\right)-3\left(x+2\right)=\left(x^2-3\right)\left(x+2\right)\)

\(a,x^2+7x+7y-y^2\)

\(=x^2-y^2+7\left(x+y\right)\)

\(=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)\)

\(=\left(x+y\right)\left(x-y+7\right)\)

\(b,x^2-2x-9y^2+6y\)

\(=x^2-\left(3y\right)^2-2\left(x-3y\right)\)

\(=\left(x-3y\right)\left(x+3y\right)-2\left(x-3y\right)\)

\(=\left(x-3y\right)\left(x+3y-2\right)\)

\(c,x^2-xy+x^3-3x^{2y}+3x^{2y}-y^3\)

\(=x\left(x-y\right)+\left(x-y\right)\left(x^2+xy+y^2\right)\)

\(=\left(x-y\right)\left(x+x^2+xy+y^2\right)\)

\(a,x^2+4x-y^2+4\)

\(=\left(x^2+4x+4\right)-y^2\)

\(=\left(x+2\right)^2-y^2\)

\(=\left(x+2-y\right)\left(x+2+y\right)\)

\(b,25-4x^2-4xy-y^2\)

\(=25-\left(4x^2+4xy+y^2\right)\)

\(=5^2-\left(2x+y\right)^2\)

\(=\left(5-2x+y\right)\left(5+2x+y\right)\)

\(c,x^3-x+y^3-y\)

\(=\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x+y\right)\)

\(=\left(x+y\right)\left(x^2-xy+y^2+1\right)\)

m, \(x^2+4x+4-4y^2=\left(x+2\right)^2-\left(2y\right)^2=\left(x+2-2y\right)\left(x+2+2y\right)\)

n, \(x^2+6xy+9y^2-4z^2=\left(x+3y\right)^2-\left(2z\right)^2=\left(x+3y-2z\right)\left(x+3y+2z\right)\)

\(x^4+x^2-27x-9\)

\(=x^4-27x+\left(x-3\right)\left(x+3\right)\)

\(=x\left(x^3-27\right)+\left(x-3\right)\left(x+3\right)\)

\(=x\left(x-3\right)\left(x^2+3x+9\right)+\left(x-3\right)\left(x+3\right)\)

\(=\left(x-3\right)\left(x^3+3x^2+10x+3\right)\)