\(45=3^2.5\\ 204=2^2.17.3\\ 126=2.3^2.7\\ \)

UCLN \(\left(a,b,c\right)=3\)

BCNN\(\left(a,b,c\right)=3^2.17.7.2^2.5=21420\)

\(\dfrac{3}{5}>\dfrac{x}{5}\\ 3>x\\ x< 3\)

mà \(x\) là số tự nhiên

=>  x \(=\left\{0,1,2\right\}\)

a, Ta có \(AB//CD\)

=> \(góc B + góc C = 180^o \)

\(=> góc C = 180^o -60^o =120 ^o\)

Áp dụng định lý tổng 4 góc trong tứ giác 

\(góc A + góc B + góc C + góc D = 360 ^o => góc A = 360 -60-80-120=100^o\)

\(\dfrac{2}{5}-\left(\dfrac{1}{10}-x\right)=\left(\dfrac{-4-5}{10}\right)^2\\ \dfrac{2}{5}-\left(\dfrac{1}{10}-x\right)=\left(-\dfrac{9}{10}\right)^2\\ \dfrac{2}{5}-\left(\dfrac{1}{10}-x\right)=\dfrac{81}{100}\\ \dfrac{1}{10}-x=\dfrac{2}{5}-\dfrac{81}{100}\\ \dfrac{1}{10}-x=\dfrac{20.2-81}{100}\\ \dfrac{1}{10}-x=-\dfrac{41}{100}\\ x=\dfrac{1}{10}-\left(-\dfrac{41}{100}\right)\\ x=\dfrac{10+41}{100}\\ x=\dfrac{51}{100}\)

\(E=\sqrt{5+2\sqrt{5}+1}-\dfrac{\sqrt{3}\left(\sqrt{5}-1\right)}{\sqrt{3}}\\ =\sqrt{\left(\sqrt{5}+1\right)^2}-\sqrt{5}+1\\ =\left|\sqrt{5}+1\right|-\sqrt{5}+1\\ =\sqrt{5}+1-\sqrt{5}+1\\ =2\)

ÁP dụng tính chất dãy tỉ số bằng nhau :

\(\dfrac{x}{10}=\dfrac{y}{6}=\dfrac{z}{21}=\dfrac{5x+y-2z}{5.10+6-2.21}=\dfrac{28}{14}=2\\ \)

=> \(\left\{{}\begin{matrix}x=2.10=20\\y=2.6=12\\z=2.21=42\end{matrix}\right.\)

\(k,\\ =\left(x-y\right)^2-9z^2=\left(x-y-3z\right)\left(x-y+3z\right)\\ l,\\ =a^3\left(a-x\right)-y\left(a-x\right)\\ =\left(a^3-y\right)\left(a-x\right)\\ m,\\ =2x^2\left(y+2z\right)+2y^2z+4xy^2+2xz^2+4yz^2+9xyz\\ =2x^2\left(y+2z\right)+\left(2y^2z+4yz^2\right)+\left(4xy^2+8xyz\right)+\left(xyz+2xz^2\right)\\ =2x^2\left(y+2z\right)+2yz\left(y+2z\right)+4xy\left(y+2z\right)+xz\left(y+2z\right)\\ =\left(2x^2+2yz+4xy+xz\right)\left(y+2z\right)\\ =\left[x\left(2x+z\right)+2y\left(z+2x\right)\right]\left(y+2z\right)\\ =\left(2y+x\right)\left(2x+z\right)\left(y+2z\right)\)

\(33,=\left(2-x\right)\left(4+2x+x^2\right)\\ 34,=\left(3+2x\right)\left(9-6x+4x^2\right)\\ 35,=\left(x^3-64\right)\\ 36,=\left(x^3-8\right)\\ 37,=4-2.2.3xy+9x^2y^2=4-12xy+9x^2y^2\\ 38,=\left(3x^2-5y\right)\left(3x^2+5y\right)\\ 39,=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\\ 40,=4x^2-12xyz+9y^2z^2\)