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\(a^3b-ab^3=ab\left(a^2-b^2\right)=ab\left(a^2-ab+ab-b^2\right)=ab\left(a-b\right)\left(a+b\right)\)
Với a hoặc b chẵn \(\Leftrightarrow ab\left(a-b\right)\left(a+b\right)⋮2\)
Với a và b lẻ \(\Leftrightarrow\left(a-b\right)⋮2\Leftrightarrow ab\left(a-b\right)\left(a+b\right)⋮2\)
Vậy \(ab\left(a-b\right)\left(a+b\right)⋮2,\forall a,b\left(1\right)\)
Với a hoặc b chia hết cho 3 thì \(ab\left(a-b\right)\left(a+b\right)⋮3\)
Với \(a=3k+1;b=3q+1\Leftrightarrow\left(a-b\right)=3\left(k-q\right)⋮3\)
\(\Leftrightarrow ab\left(a-b\right)\left(a+b\right)⋮3\)
Với \(a=3k+1;b=3q+2\Leftrightarrow\left(a+b\right)=\left(3k+1+3q+2\right)=3\left(k+q+1\right)⋮3\)
\(\Leftrightarrow ab\left(a-b\right)\left(a+b\right)⋮3\)
Mà a,b có vai trò tương đương nên \(ab\left(a-b\right)\left(a+b\right)⋮3,\forall a,b\left(2\right)\)
\(\left(1\right)\left(2\right)\Leftrightarrowđpcm\)
Ta có : a3b -ab3
=a3b -ab -ab3 +ab
=ab (a2 -1) -ab (b2 -1)
=ab (a-1)(a+1) -ab (b-1)(b+1)
Vì a (a-1)(a+1) là 3 số tự nhiên liên tiếp nên chia hết cho 6 .Tương tự b (b-1)(b+1) cũng chia hết cho 6
=> a3b -ab3 chia hết cho 6 (đpcm )
71.
\(\left\{{}\begin{matrix}BB'\perp\left(ABCD\right)\\BB'\in\left(ABB'A'\right)\end{matrix}\right.\) \(\Rightarrow\left(ABCD\right)\perp\left(ABB'A'\right)\)
74.
\(\left\{{}\begin{matrix}DD'\perp\left(ABCD\right)\\DD'\in\left(CDD'C'\right)\end{matrix}\right.\) \(\Rightarrow\left(ABCD\right)\perp\left(CDD'C'\right)\)
1. English is more interesting than music.
2. Today they are not as happy as they were yesterday.
3. Ha Noi is not as small as Hai Duong.
4. Mai's sister is not as pretty as her.
6. You have got more money than me.
7. Art is not as difficult as French.
8. Nam's father is more careful than him.
9. No one in our town is as rich as Mr Ron.
10. He is the most intelligent in my class.
11. Everest is the highest mountain in the world.
12. Minh is the fattest person in my group.
13. I can't swim as far as Jan.
14B 15C 16A 17C 18B 19C 20B
1 If Jack's watch hadn't been slow, he wouldn't have been late for the meeting
2 Heinrich wishes he had gone to art school when he was younger
3 If we lived in a big city, we could easily get access to the internet
4 She said if my job was so bad, why I didn't leave
5 Had I not used my calculator, I wouldn't have taken longer