theo dãy tỉ số bằng nhau ta có:
\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{a+b+c}{b+c+d}\)
\(\Rightarrow\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{b}.\frac{b}{c}.\frac{c}{d}=\frac{a}{d}\)
bài 1: cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\)
a) CMR: (a+2c)(b+d)=(a+c)(b+2d) \(\left(b,d\ne0\right)\)
b) CMR: (a+c)(b-d)=ab-cd
c) CMR: \(\frac{a}{a-b}=\frac{c}{c-d}\left(a,b,c,d>0;a\ne b,c\ne d\right)\)
bài 2: cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}CMR:\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
Cho: \(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}.CMR:\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
\(Cho\frac{a}{b}=\frac{b}{c}=\frac{c}{d}.cmr\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)
CMR : \(\frac{\left(a+b-c\right)^3}{a}=\frac{\left(b+c-d\right)^3}{d}\)
\(cho\frac{a}{b}=\frac{b}{c}=\frac{c}{d}.CMR:\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
\(cho:\frac{a}{b}=\frac{b}{c}=\frac{c}{d}CMR:\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{b}\)
\(cho\frac{a}{b}=\frac{c}{d}\left(b:d>0\right).CMR\frac{a}{b}=\frac{a+c}{b+d}và\frac{c}{d}=\frac{c-a}{c-d}\)
Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\) . CMR : \(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
1. cho \(\frac{a}{b}=\frac{c}{d};\)(b,c,d khac 0)
cmr: \(\frac{a-b}{a+b}=\frac{c-d}{c+d}\); \(\frac{a\cdot b}{c\cdot d}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
