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\(b,3^{n+2}-2^{n+2}+3^n-2^n⋮10\)
Ta có: \(3^{n+2}-2^{n+2}+3^n-2^n\)
\(=3^n.9-2^n.4+3^n-2^n\)
\(=3^n.10-2^n.5\)
Với: \(n\ge1\Rightarrow2^n⋮2\Rightarrow2^n.5⋮10\)
\(3^n.10⋮10\)
\(\Rightarrow3^n.10-2^n.5⋮10\)
\(\Rightarrow\)Ta có đpcm (viết ra cái đề ý)
\(d,7^6+7^5-7^4⋮11\)
Ta có: \(7^6+7^5-7^4=7^4\left(7^2+7-1\right)\)
\(=7^4\left(49+7-1\right)\)
\(=7^4.55\)
Trong tích có thừa số \(55⋮11\)
\(\Rightarrow\)Ta có đpcm (viết ra cái đề ý)
\(a,7^6+7^5-7^4=7^4\left(7^2+7-1\right)\\ =7^4\cdot55\\ \Rightarrow7^6+7^5-7^4⋮55\)
\(b,3^{n+2}-2^{n+2}+3^n-2^n\\ =3^n\cdot3^2+3^n-2^n\cdot2^2-2^n\\ =3^n\left(3^2+1\right)-2^n\left(2^2+1\right)\\ =3^n\cdot10-2^{n-1}\cdot2\cdot5\\ =10\cdot\left(3^n-2^{n-1}\right)\\ \Rightarrow3^{n+2}-2^{n+2}+3^n-2^n⋮10\)
\(c,8^7-2^{18}=8^7-\left(2^3\right)^6\\ =8^7-8^6\\ =8^6\cdot\left(8-1\right)\\ =8^5\cdot8\cdot7\\ =8^5\cdot4\cdot14\\ \Rightarrow8^7-2^{18}⋮14\)
b: \(=3^n\cdot\left(3^2+1\right)-2^n\cdot\left(2^2+1\right)\)
\(=3^n\cdot10-2^n\cdot5\)
\(=3^n\cdot10-2^{n-1}\cdot10⋮10\)
c: \(=3^n\left(3^2+3\right)+2^n\left(2^3+2^2\right)\)
\(=3^n\cdot12+2^n\cdot12⋮6\)
\(a,8^7-2^{18}=2^{21}-2^{18}=2^{17}\left(2^4-2\right)=14.2^7⋮14\)
\(b,10^6-5^7=2^6.5^6-5^7=5^6\left(2^6-5\right)=59.5^6⋮59\)
c ko nói chia hết cho số nào
\(d,3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\)
\(=3^{n+1}\left(3^2+3\right)+2^{n+1}\left(2^2+2\right)\)
\(=3^{n+1}.12+2^{n+1}.6\)
\(=6.\left(3^{n+1}.2+2^{n+1}\right)⋮6\)
\(7^6+7^5-7^4\)
\(=7^4\cdot7^2+7^5\cdot7-7^4\)
\(=7^4\cdot\left(7^2+7-1\right)\)
\(=7^4\cdot55\)
\(=7^4\cdot5\cdot11⋮11\left(đpcm\right)\)
\(7^6+7^5-7^4=7^4.\left(7^2+7-1\right)\)
\(=7^4.55⋮11\)
\(=>7^6+7^5-7^4⋮11\)
Bài 2:
1: \(5^n+5^{n+2}=650\)
\(\Leftrightarrow5^n\cdot26=650\)
\(\Leftrightarrow5^n=25\)
hay x=2
2: \(32^{-n}\cdot16^n=1024\)
\(\Leftrightarrow\dfrac{1}{32^n}\cdot16^n=1024\)
\(\Leftrightarrow\left(\dfrac{1}{2}\right)^n=1024\)
hay n=-10
13: \(9\cdot27^n=3^5\)
\(\Leftrightarrow3^{3n}=3^5:3^2=3^3\)
=>3n=3
hay n=1