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a) Ta có: \(\dfrac{a}{b}=\dfrac{c}{d}\)
\(\Leftrightarrow\dfrac{b}{a}=\dfrac{d}{c}\)
\(\Leftrightarrow\dfrac{b}{a}-1=\dfrac{d}{c}-1\)
\(\Leftrightarrow\dfrac{b-a}{a}=\dfrac{d-c}{c}\)
\(\Leftrightarrow\dfrac{a-b}{a}=\dfrac{c-d}{c}\)
\(\Leftrightarrow\dfrac{a}{a-b}=\dfrac{c}{c-d}\)(đpcm)
![](https://rs.olm.vn/images/avt/0.png?1311)
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Ta có: \(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{\left(a+b+c\right)^3}{\left(b+c+d\right)^3}=\frac{a^3+b^3+c^3+2ab+2ac+2bc}{b^3+c^3+d^3+2bc+2bd+2cd}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
đặt a/b=c/d=k =>a=bk;c=dk Thay Vào :
a.c/b.d=bk.dk/b.d=k(b.d)/b.d=k(1) (a^2+c^2)/(b^2+d^2)=(bk)^2.(dk)^2/b^2+d^2 =k^2(b^2+d^2)/b^2+d^2=k^2(2)
từ (1) và (2) =>...............
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