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1. Cho phân số a/b, b>a. C/m :
a) Nếu a/b < 1 thì a+1/b+1 > a/b
b) Nếu a/b > 1 thì a/b > a+1/b+1
2. Tính :
3/4 + 3/12 + 3/24 + 3/40 + 3/60 + 3/84 + 3/112 + 3/144 + 1/180
Toán lớp 6
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a: \(\Leftrightarrow\left(a^2-3\right)\left(a^2-10\right)< 0\)
\(\Leftrightarrow3< a^2< 10\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{3}< a< \sqrt{10}\\-\sqrt{10}< a< -\sqrt{3}\end{matrix}\right.\)
d: \(\Leftrightarrow\left(a-3\right)\left(a+1\right)< 0\)
hay -1<a<3
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(a+1)(a+2)(a+3)-a(a+1)(a+2)
= (a+3-a)(a+1)(a+2)
= 3(a+1)(a+2)
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(a + 1)(a + 2)(a + 3) - a(a + 1)(a + 2) = (a + 1)(a + 2)[(a + 3) - a] = 3(a + 1)(a + 2)
Ta có: (a+1).(a+2).(a+3) - a.(a+1).(a+2)=(a+1).(a+2).(a+3-a)=(a+1).(a+2).3
=>(a+1).(a+2).(a+3) - a.(a+1).(a+2) = 3.(a+1).(a+2)
\(\left(a-1\right)-\left(a-3\right)\)
\(=\)\(a-1-a+3\)
\(=\)\(\left(a-a\right)+\left(-1+3\right)\)
\(=\)\(0+2\)
\(=\)\(2\)