biet (a+b+c+d).(a-b-c+d)=(a-b+c-d).(a+b-c-d) chung minh a/c=b/d
Những câu hỏi liên quan
chung minh a+b/c+d=b+c/d+a (biet a+b+c+dang khac 0)
chung minh A + B = C - D
biet A =a + b - 5 , B = -b -c + 1 , C = b - c -4 , D = b - a
Ta có A+B= a+b-5-b-c+1
=a-c+(b-b)+(-5+1)
=a-c-4(1)
C-D =b-c-4-(b-a)
=b-c-4-b+a
=a-c+(b-b)+4
=a+c+4(2)
Từ (1) và (2) ta có A+B=C-D
Đúng 0
Bình luận (1)
Chung minh (a + c)^2 / a^2 - c^2 = (b + d)^2 / b^2 - d^2
Biet a/b = c/d
\(\frac{a}{b}=\frac{c}{d}=k\Rightarrow\hept{\begin{cases}a=bk\\c=dk\end{cases}}\)
Ta có : \(\frac{\left(a+c\right)^2}{a^2-c^2}=\frac{\left(a+c\right)^2}{a^2-ac+ac-c^2}=\frac{\left(a+c\right)^2}{a\left(a-c\right)+c\left(a-c\right)}=\frac{\left(a+c\right)^2}{\left(a+c\right)\left(a-c\right)}=\frac{a+c}{a-c}\)
\(=\frac{bk+dk}{bk-dk}=\frac{k\left(b+d\right)}{k\left(b-d\right)}=\frac{b+d}{b-d}\)(1)
Lại có \(\frac{\left(b+d\right)^2}{b^2-d^2}=\frac{\left(b+d\right)^2}{b^2-bd+bd-d^2}=\frac{\left(b+d\right)^2}{b\left(b-d\right)+d\left(b-d\right)}=\frac{\left(b+d\right)^2}{\left(b-d\right)\left(b+d\right)}=\frac{b+d}{b-d}\left(2\right)\)
Từ (1) (2) => \(\frac{\left(a+c\right)^2}{a^2-c^2}=\frac{\left(b+d\right)^2}{b^2-d^2}\)
Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow\hept{\begin{cases}a=bk\\c=dk\end{cases}}\)
\(\frac{\left(a+c\right)^2}{a^2-c^2}=\frac{\left(a+c\right)\left(a+c\right)}{\left(a-c\right)\left(a+c\right)}=\frac{a+c}{a-c}=\frac{bk+dk}{bk-dk}=\frac{k\left(b+d\right)}{k\left(b-d\right)}=\frac{b+d}{b-d}\)(1)
\(\frac{\left(b+d\right)^2}{b^2-d^2}=\frac{\left(b+d\right)\left(b+d\right)}{\left(b-d\right)\left(b+d\right)}=\frac{b+d}{b-d}\)(2)
Từ (1) và (2) => đpcm
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}=\frac{a-c}{b-d}\)
\(\Rightarrow\frac{a+c}{b+d}=\frac{a-c}{b-d}\)
\(\Rightarrow\frac{a+c}{a-c}=\frac{b+d}{b-d}\)
\(\Rightarrow\frac{\left(a+c\right).\left(a+c\right)}{\left(a-c\right).\left(a+c\right)}=\frac{\left(b+d\right).\left(b+d\right)}{\left(b-d\right).\left(b+d\right)}\)
\(\Leftrightarrow\frac{\left(a+c\right)^2}{a^2-c^2}=\frac{\left(b+d\right)^2}{b^2-d^2}\) ( đpcm )
Xem thêm câu trả lời
cho 5 so a, b, c, d, e. Biet a^b=b^c=c^d=d^e=e^a. chung minh 5 so do bang nhau
biet a+b+c+d chia het cho 3 . chung minh a,b,c,d chia het cho 3
biet a+b+c+d chia het cho 3 . chung minh a,b,c,d chia het cho 3
chung minh 2a+b/2a-b=2c+d/2c-d biet a/b=c/d
\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{2a}{2c}=\frac{b}{d}\)
áp dụng tính chất của dãy tỉ số bằng nhau ta có
\(\frac{2a}{2c}=\frac{b}{d}=\frac{2a+b}{2c+d}=\frac{2a-b}{2c-d}\)
\(\Rightarrow\frac{2a+b}{2c+d}=\frac{2a-b}{2c-d}\Rightarrow\frac{2a+b}{2c-d}=\frac{2c+d}{2c-d}\)
Đúng 0
Bình luận (0)
a,b,c,d>0 chung minh rang 2< (a+b)/(a+b+c)+(b+c)/(b+c+d)+(c+d)/(c+d+a)+(d+a)/(d+a+b)<3
Cho a/b =c/d. CMR :
a) a+c/b+d = a-c/b-d.
b) a-b/b = c-d/d.
Ai biet thi chi giup minh voi nhe. Minh dang can gap lam.