Ta có : \(\dfrac{a}{b}=\dfrac{c}{d}\)
➩\(\dfrac{a}{c}=\dfrac{b}{d}\)➩\(\dfrac{2008a}{2009c}=\dfrac{2009b}{2010d}=\dfrac{2008a+2009b}{2009c+2010d}=\dfrac{2008a-2009b}{2009c-2010}\)
➩\(\dfrac{2008a-2009b}{2009c+2009c}=\dfrac{2008c-2009d}{2009a+2010d}\left(đpcm\right)\)
* đpcm : điều phải chứng minh
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\(^{\dfrac{2008a-2009b}{2009c+2010d}}=\dfrac{2008c-2009d}{2009a+2010b}.\dfrac{b^2}{d^2}\)
Làm hộ mk với !!! HELP ME !!!!
Bài 1 Cho \(\dfrac{a+b+c}{a+b-c}=\dfrac{a-b+c}{a-b-c}\left(b\ne0\right)\) CMR \(c=0\)
Bài 2 Cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}CMR\left(\dfrac{a+b+c}{b+c+d}\right)^3=\dfrac{a}{d}\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\)và b, d khác 0. CMR \(\dfrac{ac}{bd}=\dfrac{a^2+c^2}{b^2+d^2}\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) .Cmr:
\(\dfrac{a+c}{b+d}=\dfrac{a-c}{b-d}\) \(\dfrac{a-c}{a+c}=\dfrac{b-d}{b+d}\)
\(\dfrac{a}{a+c}=\dfrac{b}{b+d}\) \(\dfrac{a}{a-c}=\dfrac{b}{b-d}\)
Cho \(\dfrac{bz-cy}{a}=\dfrac{cx-az}{b}=\dfrac{ay-bx}{c}\).CMR \(\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}\)
Cho : \(\dfrac{a+b}{a-b}=\dfrac{c+d}{c-d}.CMR\) \(\dfrac{a}{b}=\dfrac{c}{d}\)
\(Cho\dfrac{a}{b}=\dfrac{c}{d}CMR\left(\dfrac{a+b}{c+d}\right)^2=\dfrac{a^2-b^2}{c^2-d^2}\)
a) Cho \(\dfrac{a}{b}\)=\(\dfrac{b}{c}\)=\(\dfrac{c}{d}\)
CMR:(\(\dfrac{a+b+c}{b+c+d}\))\(^3\)=\(\dfrac{a}{d}\)
b)Cho \(\dfrac{a1}{a2}\)=\(\dfrac{a2}{a3}\)=\(\dfrac{a3}{a4}\)=...=\(\dfrac{a2008}{a2009}\)
CMR: \(\dfrac{a1}{a2009}\)=(\(\dfrac{a1+a2+a3+...+a2008}{a2+a3+a4+...+a2009}\))\(^{2008}\)
c) Cho \(\dfrac{a}{2003}\)=\(\dfrac{b}{2004}\)=\(\dfrac{c}{2005}\)
CMR: 4(a-b)(b-c)=(c-a)\(^2\)
Cho các số a, b, c, x, y, z thõa mản điều kiện \(\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}\) . CMR:
\(\dfrac{bz-cy}{a}=\dfrac{cx-az}{b}=\dfrac{ay-bx}{c}\)
