Áp dụng tính chất của dãy tỉ số = nhau ta có:
\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{a+b+c}{b+c+d}\)
=> \(\frac{a}{b}.\frac{b}{c}.\frac{c}{d}=\frac{a+b+c}{b+c+d}.\frac{a+b+c}{b+c+d}.\frac{a+b+c}{b+c+d}\)
=> \(\frac{a}{d}=\left(\frac{a+b+c}{b+c+d}\right)^3\left(đpcm\right)\)
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 \(\frac{a}{b}=\frac{c}{b}\) CM :
a )\(\left(\frac{a-b}{c-d}\right)^2=\frac{ab}{cd}\)
b ) \(\left(\frac{a+b}{c+d}\right)^3=\frac{a^3-b^3}{c^3-d^3}\)
cho \(\frac{a}{b}=\frac{c}{d}\) chứng minh rằng :\(\frac{ab}{cd}=\frac{\left(a-b\right)^2}{\left(c-d\right)^2}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
Câu 3: Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\). Chứng minh \(\left(\frac{a-b-c}{b-c-d}\right)=\frac{a}{d}\)
1) Cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\)
Chứng minh \(\frac{a}{b}=\frac{a-c}{b-d}\left(b,d\ne0\right)\)
2) Cho \(\frac{a}{b}=\frac{c}{d}\)
Chứng minh \(\frac{a+b}{a-b}=\frac{c+d}{c-d}\left(a-b\ne0;c-d\ne0\right)\)
Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{d}{a}\)\(\left(a+b+c+d\ne0\right)\)Tìm M = \(\frac{2a-b}{c+d}=\frac{2b-c}{d+a}=\frac{2c-d}{a+b}=\frac{2d-a}{b+c}\)
CMR
Nếu \(\frac{a}{b}=\frac{c}{d}\) thì \(\left(\frac{a-b}{c-d}\right)^4=\frac{a^4+b^4}{c^4+d^4}\)
Bài1: Cho \(ac=b^2;bd=c^2\)
CMR \(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
Bài2: Cho \(\frac{2a+b+c}{a}=\frac{a+2b+c}{b}=\frac{a+b+2c}{c}\)
Tính N= \(\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b}\)
GIÚP MÌNH VS!!!! ĐANG CẦN GẤP
cho \(\frac{a}{2b}=\frac{b}{2c}=\frac{c}{2d}=\frac{d}{2a}\left(a,b,c,d\ne0\right)\)
Tính \(A=\frac{2011a-2010b}{c+d}+\frac{2011b+2010c}{a+d}+\frac{2011c-2010d}{a+b}+\frac{2011d-2010a}{b+c}\)