Question

Answer 1

Bài 10:
a)
\(B=4^{20}+4^{21}+4^{22}+4^{23}\)
\(B=\left(4^{20}+4^{21}\right)+\left(4^{22}+4^{23}\right)\)
\(B=4^{20}\left(1+4\right)+4^{22}\left(1+4\right)\)
\(B=\left(1+4\right)\left(4^{20}+4^{22}\right)\)
\(B=5\left(4^{20}+4^{22}\right)\)
Vì \(5\) ⋮ \(5\)
⇒ \(B\) ⋮ \(5\)


b)
\(M=\left\{-12;-2;2;12;22;32\right\}\)


c) (Cho \(x\) ∈ \(Z\))
    \(4x+4\) ⋮ \(x-3\)
⇔\(4\left(x-3\right)+16\) ⋮ \(x-3\)
Để \(4x+4\) ⋮ \(x-3\) thì \(x-3\) ∈ \(Ư\left(16\right)\)
Ta có \(Ư\left(16\right)=\left\{\pm1;\pm2;\pm4;\pm8;\pm16\right\}\)
⇒ \(x-3=\left\{\pm1;\pm2;\pm4;\pm8\pm16\right\}\)
⇒ \(x=\left\{4;2;5;1;7;-1;11;-5;19;-13\right\}\)

\(\#PeaGea\)