Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
Do a < b < c < d < m < n
=> 2c < c + d
m< n => 2m < m+ n
=> 2c + 2a +2m = 2 ( a + c + m) < a +b + c + d + m + n)
Do đó :
\(\dfrac{\text{(a + c + m)}}{\left(a+b+c+d+m+n\right)}\) < \(\dfrac{1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu hỏi của Linh Suzu - Toán lớp 7 | Học trực tuyến, nhớ tìm trước khi hỏi, lần sau t ko tìm đâu
![](https://rs.olm.vn/images/avt/0.png?1311)
Giả sử trong 4 số a;b;c;d không tồn tại 2 số bằng nhau
Không mất tính tổng quát ta giả sử a < b < c < d
=> a2 < b2 < c2 < d2 (do a;b;c;d nguyên dương)
=> \(\frac{1}{a^2}>\frac{1}{b^2}>\frac{1}{c^2}>\frac{1}{d^2}\)
\(\Rightarrow\frac{4}{a^2}>\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+\frac{1}{d^2}=1\)
=> a2 < 4
=> a < 2 (1)
Lại có: \(\frac{1}{a^2}\)< 1 (theo đê bai)
=> a2 > 1
=> a > 1 (do a nguyên dương) (2)
Từ (1) và (2) => 1 < a < 2, mâu thuẫn với đề là a nguyên dương
Như vậy trong 4 số đã cho luôn tồn tại ít nhất 2 số bằng nhau (đpcm)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đề sai cho mình sửa lại :
Cho 6 số nguyên dương a < b < c < d < m < n
Chứng minh rằng \(\frac{a+c+m}{a+b+c+d+m+n}<\frac{1}{2}\)
Bài giải:
Ta có :a < b \(\Rightarrow\) 2a < a + b ; c < d \(\Rightarrow\) 2c < c + d ; m < n \(\Rightarrow\) 2m < m + n
Suy ra 2a + 2c + 2m = 2(a + c + m) < (a + b + c + d + m + n). Do đó
Vậy : \(\frac{a+c+m}{a+b+c+d+m+n}<\frac{1}{2}\) (đpcm)
do a<b<c<d<m<n
=> a+c+m < b+d+n
=> 2(a+c+m) < a+b+c+d+m+n
=> \(\frac{2\left(a+c+m\right)}{a+b+c+d+m+n}< 1\) => \(\frac{a+c+m}{a+b+c+d+m+n}< \frac{1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
TH1:a+b+c=0
\(\Rightarrow\left\{{}\begin{matrix}a+b=-c\\b+c=-a\\c+a=-b\end{matrix}\right.\)
\(\Rightarrow H=\dfrac{b+a}{b}.\dfrac{c+b}{c}.\dfrac{a+c}{a}=\dfrac{\left(-c\right)\left(-b\right)\left(-a\right)}{b.c.a}=-1\)
TH2:\(a+b+c\ne0\)
Áp dụng tc dãy tỉ số bằng nhau ta có:
\(\dfrac{a+b}{c}=\dfrac{b+c}{a}=\dfrac{c+a}{b}=\dfrac{2\left(a+b+c\right)}{a+b+c}=2\)
\(\Rightarrow\left\{{}\begin{matrix}a+b=2c\\b+c=2a\\c+a=2b\end{matrix}\right.\)
\(\Rightarrow H=\dfrac{b+a}{b}.\dfrac{c+b}{c}.\dfrac{a+c}{a}=\dfrac{\left(2c\right)\left(2b\right)\left(2a\right)}{b.c.a}=8\)
Vậy H=-1 hoặc H=8
c)
Ta có \(a< b< c< d< m< n\)
\(\Rightarrow\left\{{}\begin{matrix}a< b\\c< d\\m< n\end{matrix}\right.\)
\(\Rightarrow a+c+m\le b+d+n\)
\(\dfrac{a+c+m}{a+b+c+d+m+n}< \dfrac{1}{2}\)
\(\Leftrightarrow2a+2c+2m< a+b+c+d+m+n\)
\(\Leftrightarrow a+c+m< b+d+n\) ( thỏa mãn đề bài )
\(\Rightarrow\) đpcm
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu hỏi của Đinh Trần Nhật Minh - Toán lớp 7 - Học toán với OnlineMath
Em tham khảo nhé!
Do a < b < c < d < m < n
=> 2c < c + d
m< n => 2m < m+ n
=> 2c + 2a +2m = 2 ( a + c + m) < a +b + c + d + m + n)
Do đó :
(a + c + m)/(a + b + c + d + m + n) < 1/2(đcpcm)
Bạn có thể nói rõ cái chỗ này giúp mình đc ko
Cảm ơn bạn nhiều![](data:image/png;base64,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)