\(x+2x+3x+...+9x=459-3^2\) 

\(\Rightarrow9x+\left(1+2+3+...+9\right)=450\) 

\(\Rightarrow9x+\frac{\left[\left(9+1\right).9\right]}{2}=450\) 

\(\Rightarrow9x+45=450\) 

\(\Rightarrow9x=450-45\) 

\(\Rightarrow x=\frac{450-45}{9}=\frac{405}{9}=45\)

\(2^{x+3}+2^x=144\) 

\(\Rightarrow2^x\left(2^3+1\right)=144\) 

\(\Rightarrow2^x.9=144\) 

\(\Rightarrow2^x=\frac{144}{9}=16=2^4\) 

Vậy \(x=4\)

€£¥€£¥$$$£¥$£€$£¥$$€££$£$£#£$€$££$¥$£$££#£#£$£#££#£$£$££$£$£$£$£#££$£££$£$£$£$££$£$£$£$£#££#£$£#£#£#££#£$£$£#$£$££$£$€$€£$£$¥£$$€€$£$£$£$

a: \(\Leftrightarrow x-3\inƯ\left(21\right)\)

\(\Leftrightarrow x-3\in\left\{-3;-1;1;3;7;21\right\}\)

hay \(x\in\left\{0;2;4;6;10;24\right\}\)

b: \(\Leftrightarrow x-1\in\left\{1;-1;17\right\}\)

hay \(x\in\left\{2;0;18\right\}\)

c: \(\Leftrightarrow2x-1+4⋮2x-1\)

\(\Leftrightarrow2x-1\in\left\{1;-1\right\}\)

hay \(x\in\left\{1;0\right\}\)

d: \(\Leftrightarrow x^2+x+3⋮x+1\)

\(\Leftrightarrow x+1\inƯ\left(3\right)\)

\(\Leftrightarrow x+1\in\left\{1;3\right\}\)

hay \(x\in\left\{0;2\right\}\)

\(x^6-x^4+2x^3+2x^2=y^2\)

\(y^2+y=x^4+x^3+x^2+x=0\left(1\right)\)

\(\Leftrightarrow y\left(y+1\right)=x\left(x^3+x^2+x+1\right)=0\)

Ta có 4 PT

\(x1=0;y1=0\)

\(x2=0;y2=-1\)

\(x3=-1;y3=0\)

\(x4=-1;y4=-1\)