Gọi số đó là a

=> \(a-170⋮255\)

255=85\(\times\)3

\(\Rightarrow a-170⋮85\)

Vì \(170⋮85\)

\(\Rightarrow a⋮85\)

Ta có:

\(a-12⋮36\)

\(\Rightarrow\left\{{}\begin{matrix}a-12⋮4\\a-12⋮9\end{matrix}\right.\)

Vì \(\left\{{}\begin{matrix}12⋮4\\12⋮̸9\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}a⋮4\\a⋮̸9\end{matrix}\right.\)

\(A=2.4.6.8.10.12-2^3.5\)

Ta có:

\(2.4.6.8.10⋮6;8;20\)

\(40⋮8;20\)

\(\Rightarrow A⋮8;20\) và \(A⋮̸6\)

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

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

\(=-\left(x-2\right)^2-1\)

Vì \(-\left(x-2\right)^2\le0\forall x\)

=> \(G\le-1\forall x\)

\(MaxG=-1\Leftrightarrow x=2\)

\(5n+14⋮n+2\)

\(5\left(n+2\right)+4⋮n+2\)

\(4⋮n+2\)

\(n+2\inƯ\left(4\right)=\left\{1;2;4\right\}\)

\(n\in\left\{0;2\right\}\)

a) \(120+36=12\left(10+3\right)=12.13⋮12\)

b) \(120a+36b\)

\(=12.10a+12.3b\)

\(=12\left(10a+3b\right)⋮12\)

\(87-\left(73-x\right)=20\)

\(73-x=87-20\)

\(73-x=67\)

\(x=73-67\)

\(x=6\)

Sửa đề: 

\(E=x^4-2x^3+3x^2-4x+2022\)

\(=\left(x^4-2x^3+x^2\right)+\left(2x^2-4x+2\right)+2020\)

\(=\left(x^2-x\right)^2+2\left(x-1\right)^2+2020\)

Vì \(\left(x^2-x\right)^2+2\left(x-1\right)^2\ge0\forall x\)

\(\Rightarrow E\ge2020\)

\(MinE=2020\Leftrightarrow\left\{{}\begin{matrix}x^2-x=0\\x-1=0\end{matrix}\right.\)\(\Leftrightarrow x=1\)

\(Đặt\) \(A=2.2^2+3.2^3+4.2^4+...+n.2^n\)

\(2A=2.2^3+3.2^4+4.2^5+....+n.2^{n+1}\)

\(2A-A=2.2^3+3.2^4+4.2^5+....+n.2^{n+1}-\left(2.2^2+3.2^3+4.2^4+...+n.2^n\right)\)

\(=-2.2^2-2^3-2^4-...-2^n+n.2^{n+1}\)

\(=-2^2-\left(2^2+2^3+...+2^n\right)+n.2^{n+1}\)

\(=-2^2-\left(2^{n+1}-2^2\right)+n.2^{n+1}\)

\(=\left(n-1\right).2^{n+1}\)

=> \(\left(n-1\right).2^{n+1}=2^{n+16}=2^{n+1}.2^{15}\)

\(\Leftrightarrow n-1=2^{15}\)

\(\Leftrightarrow n=2^{15}+1\)